Answer
a) $f(14)\approx 2.874$
b) $x\approx 401.312$
Work Step by Step
Given $$f(x)=\sqrt[5]{x^2}=\left( x \right)^{\frac{2}{5}}.\tag{1}$$ a) Set $x= 14$ in equation $(1)$ and determine $f(14)$:
\begin{equation}
\begin{aligned}
f(14)&= \left(14 \right)^{\frac{2}{5}} \\
&\approx 2.874.
\end{aligned}
\end{equation} b) Set $f(x)=11$ in equation $(1)$ and solve for $x$:
\begin{equation}
\begin{aligned}
f(x) & =11 \\
\left( x \right)^{\frac{2}{5}} & =11 \\
\left(\left( x \right)^{\frac{2}{5}} \right)^{\frac{5}{2}}& = \left(11\right)^{\frac{5}{2}}\\
x&\approx 401.312.
\end{aligned}
\end{equation}
