Answer
a) $f(49)\approx 21.166$
b) $x= 81$
Work Step by Step
Given $$f(x)=8 \sqrt[4]{x}=8x^{\frac{1}{4}}.\tag{1}$$ a) Set $x= 49$ in equation $(1)$ to determine $f(49)$: \begin{equation}
\begin{aligned}
f(49)&=8\cdot 49^{\frac{1}{4}} \\
&\approx 6\cdot 2.64575\\
&\approx 21.166.
\end{aligned}
\end{equation} b) Set $f(x)=24$ in equation $(1)$ and solve for $x$: \begin{equation}
\begin{aligned}
f(x) & =24 \\
8x^{\frac{1}{4}}& =24 \\
x^{\frac{1}{4}} & = \frac{24}{8} \\
\left(x^{\frac{1}{4}}\right)^4& = \left(3\right)^4\\
x&=81.
\end{aligned}
\end{equation}
