If f(x) = 3x-8, what is f^-1(-4)

Question

I was given the following Piecewise function:

f(x) = 3x-18, x<0

f(x) = x²-8, 0≤x<3

f(x) = (x-2)³, x≥3

And I was asked:

What is f ^-1(-4)

It was multiple choice. The given answers were:

A: -20

B: 3/4

C: 2

D: Two minus the cubed root of 4

E: The answer cannot be determined from the information given.

I put E. What would you have said?

Answer 1

If f(a) = b then f^-1(b) = a.

Since we are looking for f^-1(-4), we must solve the equation f(x) = -4.

According to the given definition of the function, f(2) = (2)² - 8 = -4

So, since f(2) = -4, f^-1(-4) = 2.

Answer 2

-4 < 0

x = 3f^-1(x) - 18

x + 18 = 3f^-1(x)

(x + 18) / 3 = f^-1(x)

(-4 + 18) / 3) = f^-1(-4)