Answer
a) $f(5)\approx 3.344$
b) $x\approx 27.473$
Work Step by Step
Given $$f(x)=\sqrt[4]{x^3}= \left( x \right)^{\frac{3}{4}}.\tag{1}$$ a) Set $x= 5$ in equation $(1)$ and determine $f(5)$:
\begin{equation}
\begin{aligned}
f(5)&= \left(5 \right)^{\frac{3}{4}} \\
&\approx 3.344.
\end{aligned}
\end{equation} b) Set $f(x)=12$ in equation $(1)$ and solve for $x$:
\begin{equation}
\begin{aligned}
f(x) & =12 \\
\left( x \right)^{\frac{3}{4}} & =12 \\
\left(\left( x \right)^{\frac{3}{4}} \right)^{\frac{4}{3}}& = \left(12\right)^{\frac{4}{3}}\\
x&\approx 27.473.
\end{aligned}
\end{equation}
