Answer
$f^{-1} (x)=\dfrac{x}{4}$ and $g^{-1} (x)=x-6$
Work Step by Step
Interchange $x$ and $y$: $x=4y $
$\implies y=\dfrac{x}{4}$
Replace $y$ with $f^{-1} (x)$
or, $f^{-1} (x)=\dfrac{x}{4}$
Replace $g(x)$ with $y$.
$ g(x) =x+6$
Interchange $x$ and $y$: $x=y+6 $
so, $y=x-6 \implies g^{-1} (x)=x-6$
