Question

For the function f(x)=(3-4x)^2, find the inverse. Determine whether the inverse is a function.

I need to show my steps for this one as well @SolomonZelman

Answer 1

okay, first step:
replace the "f(x) with a y"

Answer 2

do this for me please

Answer 3

sorry i'm back

Answer 4

y=(3-4x)^2

Answer 5

it's alright. now, switch the y and x. (put y where x is, and put x where y is)

you get... /

Answer 6

x=(3-4y)^2

Answer 7

yes.
now take the square root of both sides (because we need to solve for y, but do
this not by changing it back)

Answer 8

\[\sqrt{x} =3-4\]

Answer 9

you forgot something next to the 4, and the \(\large\color{black}{ \pm }\) next to the \(\large\color{black}{ \sqrt{x} }\)

Answer 10

oh oops

\[\pm \sqrt{x}=3-4x\]

Answer 11

got the plus minus, but what is next to the 4?

Answer 12

oh y not x

Answer 13

yes, \(\large\color{black}{ \pm \sqrt{x}=3-4y }\)

Answer 14

subtract 3 from both sides.

Answer 15

\[\pm \sqrt{x}-3=-4y\]

Answer 16

now, divide both sides times -4.

Answer 17

\[\frac{ \pm \sqrt{x}-3 }{ -4 }\]

Answer 18

yes,
\(\large\color{black}{ y=(\pm \sqrt{x}-3)/(-4) }\)

Answer 19

we can re-write it though.

Answer 20

\(\large\color{black}{ y=(\pm \sqrt{x}-3)/(-4) }\)

\(\large\color{black}{ y=(-1)(\pm \sqrt{x}-3)/(4) }\)

\(\large\color{black}{ y=(\mp \sqrt{x}+3)/(4) }\)

\(\large\color{black}{ y=(3\mp\sqrt{x})/(4) }\)

Answer 21

and then, this would be same as, \(\large\color{black}{ y=(3\pm\sqrt{x})~/~4 }\)

Answer 22

I can't scroll on it

Answer 23

anyways, here is the graph.
https://www.desmos.com/calculator/rdmctudroq

Answer 24

is it a function?

Answer 25

yes?

Answer 26

does it pass the vertical line test?

Answer 27

saying, is there (ever on the function) more than 1 point with the same x-coordinate, or on the same vertical line

Answer 28

I dont know, when i graphth original it is goung up

Answer 29

https://www.desmos.com/calculator/yowqmozzja

Answer 30

this is what I refer to a vertical line test.

if I draw a vertical line, will 2 points on a function be on it?

Answer 31

if 2 points (or more), that are on a function, are on a vertical line, then this function is NOT a function.

Answer 32

if on any vertical line, there is only one point, then it is a function.

Answer 33

ok

Answer 34

I have to lave for about an hour.

Answer 35

ok, is the screenshot right though with the steps before you go?

Answer 36

@SolomonZelman

Answer 37

I couldn't scroll to see all steps on the screnshot

Answer 38

I am near the comp, but I am doing some other activity now though...

Answer 39

the only thing above is the initial equation nothing is needed to be scrolled. You can see everything i put in the thingy

Answer 40

there are some mistakes, try to go over and repost.

Answer 41

in your last step, you should have a positive 4 on the bottom