Question

For the function f(x) = (3 - 4x)^2, find f^(-1). Determine whether f^(-1) is a function.

Answer 1

@wio

Answer 2

Solve for \(x\).

Answer 3

Wouldn't I plug -1 in for x ?

Answer 4

Nope. They want you to find the inverse.

Answer 5

no no no. That you would do when you are asked for f(-1)
But there you are asked for the inverse function. so u solve for x

Answer 6

Okay, so... would it be (x - 3/4)^2 ?

Answer 7

y = (3-4x)^2
sqrt(y) = 3-4x
4x = 3 - sqrt(y)
x = (1/4)(3 - sqrt(y))

Therefore
f^-1(x) is

\[(3-\sqrt{x}) / 4\]

Answer 8

Okay, so would that make f^(-1) a function? @Saikam

Answer 9

no. because it gives you 2 different values for single x. Technically, its not a function.

Answer 10

If y^2 = x

then y = sqrt(x) or y = -sqrt(x)

This means that y^2 = x is not a function because plugging in positive x values (say x = 4) gives you more than one y value.

Answer 11

Okay, last question for tonight I promise!

What value completes the square for the expression? \[x ^{2} - 12x\]

Answer 12

I know that x^2 + 12 is 36, would this be -36 or would it change the whole thing since this is subtraction?

Answer 13

I meant x^2 + 12x is 36, sorry

Answer 14

Similar Problem:

x^2 - 8x

take half of -8 to get -4, square -4 to get 16

so you add 16 to the expression above to make it a perfect square

so x^2 - 8x + 16 is a perfect square

Answer 15

well it is a multiple chice question. It's either 6, -6, 36 or -36

Answer 16

*choice

Answer 17

do you see how I got 16 in the example problem x^2 - 8x ?

Answer 18

from 4^2 ?

Answer 19

(-4)^2 actually, you're close

Answer 20

Oh okay

Answer 21

you follow the same steps to find the answer to this problem

Answer 22

so half of -12 is -6 right? so it would be -6^2 which would be 36?

Answer 23

(-6)^2 = 36, yes you got it right

Answer 24

Okay, thank you so much for all of your help! Have a good night everyone (: