Answer
a) $f(11)= 4$
b) $x= 59$
Work Step by Step
Given $$f(x)=\sqrt{x+5}.\tag{1}$$ a) Set $x= 11$ in equation $(1)$ and determine $f(11)$:
\begin{equation}
\begin{aligned}
f(11)&=\sqrt{11+5} \\
&=\sqrt{16}\\
&=4.
\end{aligned}
\end{equation} b) Set $f(x)=8$ in equation $(1)$ and solve for $x$:
\begin{equation}
\begin{aligned}
f(x) & =8 \\
\sqrt{x+5}& =8 \\
\left(\sqrt{x+5}\right)^2& = \left(8\right)^2\\
x+5&=64\\
x&= 64-5\\
x&= 59.
\end{aligned}
\end{equation}
