Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

The functions $f(x)$ and $g(x)$ are known as inverse functions. Thus, we simplify $(f\circ g) (x)=(g\circ f) (x)$ or, $f[g(x)]=g[f(x)]$ as follows: $(f\circ g) (x) =f[g(x)]=f [\dfrac{(4-x)}{3}]=4-3 [\dfrac{(4-x)}{3}] =4-(4-x)=x$ and $(g\circ f) (x) = g[f(x)]=g(4-3x)=\dfrac{1}{3}[4-(4-3x)]=\dfrac{1}{3}[4-(4-3x)]=x$ Hence, verified.