Question

1. if $g(x) = 3x - 4$, what is the value of $g^{-1}(g(-2))$?

options: $\frac{2}{3}$, $-2$, $\frac{x + 4}{3}$, $-10$

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 \( g(x) \).

Step2: Apply the property to the given problem

We are asked to find \( g^{-1}(g(-2)) \). Using the property \( g^{-1}(g(x)) = x \), we substitute \( x = -2 \). So \( g^{-1}(g(-2))=-2 \).

Answer:

-2