Answer
a) $f(45)= 12.847$
b) $x= 32$
Work Step by Step
Given $$f(x)=6 \sqrt[5]{x}= 6x^{\frac{1}{5}}.\tag{1}$$ a) Set $x= 45$ in equation $(1)$ and determine $f(45)$.
\begin{equation}
\begin{aligned}
f(45)&=6\cdot 45^{\frac{1}{5}} \\
&\approx 6\cdot 2.14113\\
&\approx12.847.
\end{aligned}
\end{equation} b) Set $f(x)=12$ in equation $(1)$ and solve for $x$: \begin{equation}
\begin{aligned}
f(x) & =12 \\
6x^{\frac{1}{5}}& =12 \\
x^{\frac{1}{5}} & = \frac{12}{6} \\
\left(x^{\frac{1}{5}}\right)^5& = \left(2\right)^5\\
x&=32.
\end{aligned}
\end{equation}
