Answer
$58$ millions kilometers
Work Step by Step
Given
$$ f(x)=0.2 x^{\frac{3}{2}}$$
Set $f(x)= 88$ and solve for $x$.
\begin{equation}
\begin{aligned}
f(x)&=88\\
0.2 x^{\frac{3}{2}}& = 88\\
x^{\frac{3}{2}}& = \frac{88}{0.2}\\
x^{\frac{3}{2}}& =440\\
\left( x^{\frac{3}{2}}\right)^{\frac{2}{3}}&= \left(440\right)^{\frac{2}{3}}\\
x&= \sqrt[3]{440^2}\\
&= 58
\end{aligned}
\end{equation}
The average distance of Mercury from the sun is about $58$ millions kilometers.
