Question

Let f(x) = x2 - 16. Find f-1(x).

Answer 1

let y be f(x)

Answer 2

\[
x=f(f^{-1}(x))=[f^{-1}(x)]^2-16
\]

Answer 3

therefor y=x2-16

Answer 4

y+16=x2

Answer 5

@Nurialozza96 what would be the first step?

Answer 6

root(y+16)=y
therefore f-1(x)=root(x-16)

Answer 7

got it?

Answer 8

@UditKulka Are you trying to prevent learning?

Answer 9

@Nurialozza96 Do you still need help?

Answer 10

A little, Im not so sure of what im doing here /:

Answer 11

\[
x=[f^{-1}(x)]^2-16
\]
First... do you want to add multiply or what?

Answer 12

multiply

Answer 13

There is nothing to multiply right now.

Answer 14

Actually when isolating, the first thing you want to do is add/subtract.

Answer 15

+16?

Answer 16

\[
x+16=[f^{-1}(x)]^2
\]

Answer 17

thren im guessing you square root it

Answer 18

right?

Answer 19

Yes.

Answer 20

I got it ! is there a rule behind these problems ? seems to be ..

Answer 21

Okay do you know the order of operations?

Answer 22

Paranthesis exponent multiply divide add subtract ?

Answer 23

Yes.
When doing these problems, you want to do it in reverse order.

Answer 24

ohh ok ok (: thankyou

Answer 25

what about Let f(x) = x - 2 and g(x) = x2 - 7x - 9. Find f(g(-1)

Answer 26

@henryarias5 Ask a separate question.

Answer 27

Anyway, in this case we have: \[
|f^{-1}(x)|=\sqrt{x+16}
\]

Answer 28

This means that: \[
f^{-1}(x)=\sqrt{x+16}\quad\text{and} \quad -\sqrt{x+16}
\]

Answer 29

This is NOT a function because it has two outputs.
Technically this function does not have an inverse function.