Question

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

Answer 1

f-1(x) represents the inverse function of f(x). The easiest way to do this is through a little cheap trick: switch the f(x) and x positions on the function and then isolate f(x).

You're given that f(x) = x^2 - 16

Switch f(x) and x.

x = f(x)^2 - 16

Now isolate f(x).

f(x)^2 = x + 16
f(x) = ±√(x + 16)

Now simply erase f(x) and rewrite it as f-1(x), since this is now the inverse function of f(x).

f-1(x) = ±√(x + 16)

NOTE: Don't forget, when taking the square root, always remember to put ± before the expression!

Answer 2

f^(-1) (x) is the inverse function of f.

To find the inverse function, interchange x with y, and y with x, AND then solve for y.

so the inverse will be x = y^2 - 16

now we solve for y, we get
y^2 = x + 16
y = + or - sqrt(x+16)

NOTE: The inverse y = +/- sqrt(x+16) is NOT a function.

The inverse of a function NEED NOT be a function, as demonstated in this exercise.