Answer
The functions f and g are inverse functions of each other.
Work Step by Step
Suppose the available expression is:
$f\left( x \right)=\frac{9}{5}x+32$ and $g\left( x \right)=\frac{5}{9}(x-32)$
Now solve for$f\left( g\left( x \right) \right)$
$f\left( g\left( x \right) \right)=$$\frac{9}{5}\left( \frac{5}{9}\left( x-32 \right) \right)+32$
$f\left( g\left( x \right) \right)=x$ …. (1)
Again solve for $g\left( f\left( x \right) \right)$
$g\left( f\left( x \right) \right)=\frac{5}{9}\left( \left( \frac{9}{5}x+32 \right)-32 \right)$
$g\left( f\left( x \right) \right)=x$ …. (2)
But, from (1) and (2) $g\left( f\left( x \right) \right)=f\left( g\left( x \right) \right)=x$
So, f and g are inverse functions to each other.
Thus, the functions f and g are inverse functions of each other.