Answer
$f(g(x)) = x$ and $g(f(x)) = x$; therefore, both functions are inverse of one another.
Work Step by Step
$$f(x) = \frac{9}{5}x +32$$ $$g(x) = \frac{5}{9}(x-32)$$
Since the condition for inverse functions is that $h(h^{-1}(x)) = x$, we can check in the following
manner: $$f(g(x)) = \frac{9}{5}(\frac{5}{9}(x-32)) +32$$ $$f(g(x)) = \frac{9}{5}(\frac{5}{9}x-\frac{160}
{9})) +32$$ $$f(g(x)) = x- 32 +32 = x$$ $$AND$$ $$g(f(x)) = \frac{5}{9}((\frac{9}{5}x +32)-32)$$ $$g(f(x)) = x +\frac{160}{9} -\frac{160}{9} = x$$
