Answer
$f^{-1}(x)=2x+2$
The graph of both functions is shown below:
Work Step by Step
$f(x)=\dfrac{1}{2}x-1$
Substitute $f(x)$ by $y$:
$y=\dfrac{1}{2}x-1$
Solve this expression for $x$. Begin by taking $-1$ to the left side:
$y+1=\dfrac{1}{2}x$
$\dfrac{1}{2}x=y+1$
Take $2$ to multiply the right side:
$x=2y+2$
Interchange $x$ and $y$:
$y=2x+2$
Substitute $y$ by $f^{-1}(x)$:
$f^{-1}(x)=2x+2$
