Question

1. if $g(x) = 3x - 4$, what is the value of $g^{-1}(g(13))$?

options: $dfrac{17}{3}$, $dfrac{x + 4}{3}$, $13$, $35$

Explanation:

Step1: Recall the property of inverse functions

For a function \( g(x) \) and its inverse \( g^{-1}(x) \), the composition \( g^{-1}(g(x)) = x \) for all \( x \) in the domain of \( g \).

Step2: Apply the property to the given problem

We are asked to find \( g^{-1}(g(13)) \). Using the property of inverse functions, we know that \( g^{-1}(g(13)) = 13 \).

Answer:

13