If f(x) = 3x + 2, find f(f^–1(14)).

Question

Is the answer 4 or 14?

Answer 1

f(x) = 3x + 2

x = 3f^-1(x) + 2

x - 2 = 3f^-1(x)

(x - 2) / 3 = f^-1(x)

(14 - 2) / 3 = f^-1(14)

12 / 3 = f^-1(14)

4 = f^-1(14)

Answer 2

Mark did not finish the question.  The inverse is 4, and f(4) = 14, so the answer is 14.

 

Note that, with any continuous, monotone increasing function f, the inverse exists and f(f^-1(x)) = f^-1(f(x)) = x

 

Thus, you didn't even need to calculate the inverse.