WEBVTT
Kind: captions
Language: en
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lets do some review stuff
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so whats going to be on the exam?
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its gonna be some f of x stuff, you know f of x
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g of x
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putting together taking the apart
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theres gonna be domain and, no range just domain
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finding inverse of functions
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ill write these down, okay your gonna need to know
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f of x stuff
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that is domain
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inverse
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composition
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composition is f of g and g of f, that kind of stuff
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your going to have umm
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trigonometry your gonna need to know
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special angles
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the 6 trig functions
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and your gonna have some word problems
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i think thats about it
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composition is when you do f of g of x or g of f of x
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oh your gonna have to do some of quations stuff here, gonna have to do f of x plus h
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minus f of x
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trigonometry lets see we did the 6 functions, soh cah toa
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we did the word problem
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i think thats pretty much whats on the exam
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i cant really think of anything else we can do it
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theres not gonna be transformations on the test
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i know that makes you sad
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i can add them now at the last minute, no?
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so lets practice some stuff
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theres 172 questions on the exam each of them have 6 parts
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some of them have sub parts
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i forget its like 9
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its about 4, dont hold me the number cause i dont have them with me
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theres about 4 for the minimum confidence part
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and then theres like four or 5 for the advance part
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so remember your first goal is to pass minimum confidence
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you guys should be able to do that just fine
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once you did that you lock in your minimum stuff
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and now you go to the advance stuff
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shouldnt be to bad
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not a lot of meterial on the test i didnt want to make it to hard
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sorta ad, do i actually feel bad?
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i dont feel bad
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i can go to sleep at night knowing youre crying
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suppose you would have
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f of x equals
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and g of x
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ugh why dont you find
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alright heres three things to do
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that should keep ypu busy for a couple minutes
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so we ask for g of f of 2
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what do you have to do?
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so you have g of x of 2
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first you have to find f of 2
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f of 2 equals 5 times 2 cubed
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minus 4 times 2 plus 1
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i think thats 33
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then you fin g of 33
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which is 2
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over 33 minus
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6
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which is 2/27
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thats fine thats 27
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you get that one? good
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f of g of h
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now we go the other way first we find g of 8
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then it equals 2/8-6 i think that equals 1
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and then f of 1
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is 5 times 1 cubed
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minus 4 times 1
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plus 1 equals 2
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everybody happy so far
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if i ask for f of g of x which i didnt ask for
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now what would i do, if we do f of g of x
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you take g of x and put it inside f of x
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that would be 5
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times
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2/x-6 cubed
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minus 4 times 2/x-6
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plus 1 and you dont have to simplfy that
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thats very hard to simplfy
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yes you want to simplify
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i can show you g of g how bout i show you that oin friday
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gonna throw one to
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if you want to find
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f of f or g of g you literally take f
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and put that in where ever theres x
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so if you were doing f of f of x
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everytime you have an x here you ave to put in
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5x cubed minus 4x plus 1
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and here if you have g of g, where x
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you put 2/x but im not concerned about those
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alright if you want to do g of f of x
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now you do it the other way, where ever theres an x
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you put in f
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so thats 5x cubed minus 4x minus 1
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minuss 6
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so far so good?
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now i just realized the inverse is really hard to find
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wow alright ignore that and for those of you watching this at home on the video
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were not gonna do that problem were gonna do a different one
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its hard to solve because its a cubic
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i think that if you think you go that answer yu didnt
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im not gonna insult anybody but youd have to isolate
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y and the cubic which means youll have to solve the cubic which is quite messy
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so i wasnt concentrating on that alright so lets give you a simpliafr one
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okay lets say f of x
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5x cubed minus 4 now find the inverse
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and what are you gonna do youre gonna switch x and y and isolate y
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alright im gonna let y equal 5x cubed minus 4
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switch x and y
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and isolate y
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how would we isolate y? well first wed add 4 to both sides
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and we would divide by 5
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x+4
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over 5
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equals y cubed then you would take the cubed root
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in fact f inverse of x, and thats all youd have to write
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so on your exam theres going to be a box
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for every question where you put in the answer
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so the tas are gonna grade
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100s of your exams, each ta gets a question
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so you get consistancey, so the tas are gonna get tired
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theyre not gonna fight you way through all your scribbling
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so make sure you put your answer in the box so they can find your answer
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cause many of you come back to us and say see over here theres my answer
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its not neccasarily going to fly
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thats all your gonna have to write nothing more complicated then that
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so we got the idea of these
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lets do a domain problem
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alright so theres 4 different f of x's
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find the domain
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alright so four different types of things where were going to find the domain
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but they have the square root notice its the square root not the cubed root
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you can take the cubed root of anything you want, you can take the odd root
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of any positive negative or zero
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right all real numbers
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so if thats the cubed root of 8x-2 would be 0
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but it does if it the square root of 2
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well all you do is 8x-2
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has to be greater then or equal to 0
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well is 8x-2 is greater then 0
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the 8x has to be greater then or equal to 2
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x has to be greater then or equal to 2/8
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or
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x has to be greater then 1/4
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now im sure your gonna ask me
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do i have to put this in interval notation
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no as said before
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but just in case you dont have to do interval notation you should know interval notation
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and you should love interval notation
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well you dont have to love it you just have to know it
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but you dont have to do it on the exam
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and if your tas says you do welll
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you dont
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every once in a while i get oh may ta said to do, well
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im in charge
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i get to decide
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f of x is 1/5 plus 1
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what can you not do with 1/5xplus1
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you cant have 0 in the denominator
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so any ration expression
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the denominator cannot be 0
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the numerator can be 0 but in this case its always 1
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so 5x plus 1
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cannot equal 0
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so x cannot equal
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-1/5
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how we doing so far? 2 for 2
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now for the entertaining ones, what if i combine theses
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so if you have f of x is
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square root of 8x plus 2
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over 5x+1
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now you have 2 problems
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the square root that still cant be
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negative you still cant get the square root of negative
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so 8x plus 2
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still has to equal 0 so x has to be greater then or equal to a quarter right
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that should be minus 2
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how did that magically become plus two oh well plus 2
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so thats minus a quarter
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and also
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x cannot equal -1/5
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so you need both of those
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you technically should write the word and
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why did i get ride of the radical here?
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well remember you cant take the square root of a negative numbe
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so to find the domain you just take whats under the radical
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and that has to be greater then or equal to 0,
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just trying to figure out what to plug in
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what youre allowed to take the square root of
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so youre not allowed to take the square root of negative numbers so you take this
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has to be greater then or equal to 0
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so both of these have to be true
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now what about the other way around what if i had f of x
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is 5x plus 1
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ovr square root of
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8x plus 2
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now he square root of 8x plus 2 again
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you cant take the square root of a negative number
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this also cant be 0 now
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because then you have 0 in the denominator
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so 8x plus 2
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has to be greater then 0
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x has to be greater then -4
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so it cant equal -1/4
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because if it equal a negative 1/4
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youd have 0 in the denominator and you cant have 0 in the denominator
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should i repeat that?
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when you see the square root you cant take the square root of a negative number
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so just as before
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8 x plus 2 is greater then or equal to 0
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and thats greater then or equal to -1/4 however
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when x equals negative 1/4 you now
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have 0 in the denominator
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and you cant have 0 in the denominator
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so you have to throw that one number out
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and you just have greater then -1/4
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so thats the different from having the radical in the numerator
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and radical in the denominator
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in the numerator you can have 0
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but in the denominator you cant have 00
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so you only have greater then sign
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so range changes just a little bit
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now we have 0 in the numerator
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you can have 0 in the numerator so this you can ignore
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make sure you understand the differnece
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amoung the four of these
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lets do something else
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suppose f of x is 6x squared plus 4
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suppose f of x squared plus 4
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find f of x plus h minus f of x
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alright so if this is f of x and f of x plus
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is 6 x plus h
00:17:24.100 --> 00:17:24.660
squared
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plus 4
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now we wnat the difference between the 2
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so you go this one minus
00:17:50.520 --> 00:17:52.280
multiply that out you get 6
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times x squared plus 2xh plus h squared
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plus 4 minus 6x squared
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minus 4
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so thats what you get when you foil out the x plus h
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now distribute you get 6x suqared
00:18:15.460 --> 00:18:16.100
plus 12x h
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plus 6/h squared
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plus 4 minus 6x squared minus 4
00:18:29.920 --> 00:18:34.160
the 6 x squared cancel and the 4s cancel because i said to you guys
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the only thing left the only terms left
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the only that contain at least 1 h
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so these cancel and these cancel so you get 12x
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h plus 6h squared
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lets try one more make a messier one
00:18:58.420 --> 00:19:00.980
see i like to do an easy one and a hrad one
00:19:17.380 --> 00:19:18.740
find f of x of that one
00:19:21.880 --> 00:19:22.760
so f of x plus h
00:19:30.280 --> 00:19:32.200
4 x plus h cubed minus 3x plus h
00:19:33.920 --> 00:19:34.420
plus 5
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so were gonna take this one and subtract this one
00:19:41.940 --> 00:19:44.260
so 4 xplus h cubed is x cued minus 3xh
00:19:47.200 --> 00:19:48.320
plus 3xh squared
00:19:49.140 --> 00:19:49.940
plus h cubed
00:19:52.080 --> 00:19:53.200
minus 3x minus 3h
00:19:54.960 --> 00:19:55.760
plus 5 minus
00:19:57.640 --> 00:19:58.920
4x suqraed minus 3x
00:19:59.960 --> 00:20:00.460
plus 5
00:20:03.340 --> 00:20:04.380
that is 4x cubed
00:20:05.200 --> 00:20:05.700
plus 12
00:20:06.940 --> 00:20:07.660
x squared h
00:20:10.700 --> 00:20:11.580
12 x h squared
00:20:12.580 --> 00:20:13.080
plus 4h
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minus 3x minus 3h
00:20:18.560 --> 00:20:20.960
that was cubed that would be 4x cubed
00:20:23.380 --> 00:20:24.340
plus 3x minus 5
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cancle the 5 the 3x
00:20:32.880 --> 00:20:35.040
and youre left with 12x squared h
00:20:36.540 --> 00:20:37.100
plus 12 x
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h squared
00:20:40.760 --> 00:20:43.560
plus 4h cubed you do not have to factor that
00:20:43.560 --> 00:20:47.780
alright everyione get that? okay wednesday we will do trig stuff