Question

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

Answer 1

F-1(x) = √(x + 16).

Explanation:

Let y = x^2 - 16

First make x the subject:

x^2 = y + 16

x = √(y + 16)

Now replace x by the inverse f-1(x) and replace y by x:

f-1(x) = √(x + 16).

Note we only take the positive square root otherwise we would not have a function.

Answer 2

See below.

Explanation:

`f(x) = x^2 - 16`

Replace f(x) with y.

`y = x^2 - 16`

Switch x and y.

`x = y^2 - 16`

Solve for y.

`y^2 = x + 16`

`y = \pm√(x + 16)`

Replace y with f^(-1)(x).

`f^(-1)(x) = \pm√(x + 16)`

The relation above is not a function, so the given function f(x) does not have an inverse unless the domain is restricted.