Answer
a) $f(81)= 22.50$
b) $x= 1194.3936$
Work Step by Step
Given $$ f(x)=2.5 \sqrt{x}.\tag{1}$$ a) Set $x= 81$ and use equation $(1)$ to determine $f(81)$: \begin{equation}
\begin{aligned}
f(81)&=2.5 \sqrt{81} \\
&=2.5\cdot 9\\
&=22.50.
\end{aligned}
\end{equation} b) Set $f(x)=86.4$ is equation $(1)$ and solve for $x$: \begin{equation}
\begin{aligned}
f(x) & =86.4 \\
2.5 \sqrt{x}& =86.4 \\
\sqrt{x} & = \frac{86.4}{2.5} \\
\left(\sqrt{x}\right)^2& = \left(34.56\right)^2\\
x&=1194.3936.
\end{aligned}
\end{equation}
