Question

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

A. 17/3

B. 35

C. x+4/3

D. 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.