Seth A.

asked • 13d# If f(x) = 3x-8, what is f^-1(-4)

I was given the following Piecewise function:

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

f(x) = x^{2}-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?

## 2 Answers By Expert Tutors

Mark M. answered • 13d

Retired math prof. Very extensive Precalculus tutoring experience.

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.

Seth A.

How would we have known to plug it into the second equation? How would we have known to try 2?13d

Mark M.

13d

Mark M. answered • 13d

Mathematics Teacher - NCLB Highly Qualified

-4 < 0

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

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

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

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

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Seth A.

Apologies, it is 3x-8, not 3x-18. I agree that the answer would be 4/3, but that was not an answer13d