Question

Let f(x) = x^2 - 16. Find f-1(x).

Answer 1

first step: change f(x) into y \[\implies y = x^2 - 16\]
now do you know how to isolate x in this equation?

Answer 2

Hint set y = f(x) to get

y = x^2 - 16

Swap x and y to get

x = y^2 - 16

Now isolate and solve for y

Finally replace the y variable with f^{-1}(x) after isolation

Answer 3

i'm stuck at the step where its √x = √y^2 - 16 i know the x becomes x^2 but i don't know what to do with the other side. and from there.

Answer 4

Well, for one, you forgot to swap x and y. Secondly, you're supposed to add 16 to both sides afterwards. then you take the square root.

Answer 5

Now all you have to do is remember this general rule

\(x = \pm \sqrt{a}\)

Answer 6

so would it be \[\pm 4 \sqrt{x}\] ?

Answer 7

no, you didn't follow the steps properly

Answer 8

You cannot reduce the square root of an addition

Answer 9

\[\pm \sqrt{x + 16}\] then?

Answer 10

good job

Answer 11

Don't forget to set that equal to the inverse of the function