See the explanation
In this exercise, we have the following functions:
[tex]f(x)=\frac{-12-2x}{3} \\ \\ g(x)=\frac{-5+6x}{5}[/tex]
So let's verify if the functions are inverses of each other.
Let's take function [tex]g[/tex]:
Step 1. Replace [tex]g(x)[/tex] by [tex]y[/tex]:
[tex]y=\frac{-5+6x}{5}[/tex]
Step 2. Interchange [tex]x[/tex] and [tex]y[/tex]:
[tex]x=\frac{-5+6y}{5}[/tex]
Step 3. Solve for [tex]y[/tex]:
[tex]x=\frac{-5+6y}{5} \\ \\ 5x=-5+6y \\ \\ 6y=5x+5 \\ \\ y=\frac{5x+5}{6}[/tex]
Step 4. Replace [tex]y[/tex] by [tex]g^{-1}(x)[/tex]:
[tex]g^{-1}(x)=\frac{5x+5}{6}[/tex]
Since:
[tex]f(x)\neq g^{-1}(x)[/tex]
Then they aren't inverse functions.
Symmetry of inverse functions: https://brainly.com/question/12253822
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