Answer
The pair of provided functions are inverses of each other.
Work Step by Step
$f\left( x \right)=1.4{{x}^{3}}+3.2$ and $g\left( x \right)=\sqrt[3]{\frac{x-3.2}{1.4}}$
Now, apply the formula for the composition of two functions
$f\circ g\left( x \right)=f\left( g\left( x \right) \right)$
Substitute $\sqrt[3]{\frac{x-3.2}{1.4}}$ for $g\left( x \right)$ in the above equation
$f\circ g\left( x \right)=f\left( \sqrt[3]{\frac{x-3.2}{1.4}} \right)$
Substitute $\sqrt[3]{\frac{x-3.2}{1.4}}$ for $x$ in the provided function $f\left( x \right)$; the above equation becomes
$\begin{align}
& f\circ g\left( x \right)=1.4\times {{\left( \sqrt[3]{\frac{x-3.2}{1.4}} \right)}^{3}}+3.2 \\
& =1.4\times \left( \frac{x-3.2}{1.4} \right)+3.2 \\
& =x-3.2+3.2 \\
& =x
\end{align}$
Since the compositions equal x, the functions are inverses.
