Answer
a) $f(50)\approx 5.831$
b) $x= 31$
Work Step by Step
Given $$f(x)=\sqrt{x-6}.\tag{1}$$ a) Set $x= 40$ in equation $(1)$ and determine $f(40)$.
\begin{equation}
\begin{aligned}
f(40)&=\sqrt{40-6} \\
&=\sqrt{34}\\
&\approx 5.831.
\end{aligned}
\end{equation} b) Set $f(x)=5$ in equation $(1)$ and solve for $x$:
\begin{equation}
\begin{aligned}
f(x) & =5 \\
\sqrt{x-6}& =5 \\
\left(\sqrt{x-6}\right)^2& = \left(5\right)^2\\
x-6&=25\\
x&= 25+6\\
x&= 31.
\end{aligned}
\end{equation}
