Answer
$f^{-1}(x)=2x+10$
Work Step by Step
Given \begin{equation}
f(x)=\frac{1}{2} x-5.
\end{equation}
Let $y= \frac{1}{2} x-5 $. Solve for $x$ in terms of $y$.
\begin{equation}
\begin{aligned}
\frac{1}{2} x-5 & = y\\
\left(\frac{1}{2} x-5\right)\cdot 2 & = y\cdot 2\\
x-10 & =2y\\
x= 2y+10.
\end{aligned}
\end{equation} Interchange $x$ and $y$. That is, set $y= 2x+10$. The inverse of the function is :
\begin{equation}
f^{-1}(x)=2x+10.
\end{equation}
