Answer
The $f\left( g\left( x \right) \right)$ and $g\left( f\left( x \right) \right)$ of the function $f\left( x \right)=2-5x$ and $g\left( x \right)=\frac{2-x}{5}$ is $f\left( g\left( x \right) \right)=x\text{ and }g\left( f\left( x \right) \right)=x$ respectively, and f and g are inverses of each other.
Work Step by Step
Now, consider the function,
$\begin{align}
& f\left( g\left( x \right) \right)=f\left( \frac{2-x}{5} \right) \\
& =2-5\left( \frac{2-x}{5} \right) \\
& =2-2+x \\
& =x
\end{align}$
Next consider the function,
$\begin{align}
& g\left( f\left( x \right) \right)=g\left( 2-5x \right) \\
& =\frac{2-\left( 2-5x \right)}{5} \\
& =\frac{5x}{x} \\
& =x
\end{align}$
This shows that $f\text{ and }g$ are inverses of each other.
Therefore, the $f\left( g\left( x \right) \right)$ and $g\left( f\left( x \right) \right)$ of the function $f\left( x \right)=2-5x$ and $g\left( x \right)=\frac{2-x}{5}$ is $f\left( g\left( x \right) \right)=x\text{ and }g\left( f\left( x \right) \right)=x$ respectively, and f and g are inverses of each other.
