Answer
$f(g(x))=\frac{3x-40}{7}$ and $g(f(x))=\frac{3x-4}{7}$.
Work Step by Step
$f(x)=3x-7, g(x)=\frac{x+3}{7}$
$f(g(x))=3\left(\frac{x+3}{7}\right)-7=\frac{3x-40}{7}$
and
$g(f(x))=\frac{3x-7+3}{7}=\frac{3x-4}{7}$.
$f(g(x))\ne g(f(x))\ne x.$
Thus, $f(x)$ and $g(x)$ are not Inverse of each other.
