Question

If g(x) = 3x − 4, what is the value of g−1(g(13))?

Answer 1

The function g(x) = 3x-4 is a linear function. Therefore the inverse does exist (which is also linear)

Because we have an inverse, this means we can use the rule 
$g^{-1}(g(x)) = x$

Replace x with 13
$g^{-1}(g(x)) = x$
$g^{-1}(g(13)) = 13$

The answer is choice D

Answer 2

The function g takes some input x from the *domain* and maps it to some value g(x) in the *range*. The function g^-1 takes some value g(x) from the *range* and maps it back to its associated value x in the *domain*. Essentially, when you feed an input through a function, and then feed that output through its inverse function, you get the original input back. So your answer here would be D. 13, since that was your original input.