Answer
$f^{-1}(x)=-2x+4$
The graph of both functions is shown below:
Work Step by Step
$f(x)=-\dfrac{1}{2}x+2$
Substitute $f(x)$ by $y$:
$y=-\dfrac{1}{2}x+2$
Solve this expression for $x$. Begin by taking $2$ to the left side:
$y-2=-\dfrac{1}{2}x$
$-\dfrac{1}{2}x=y-2$
Take $-2$ to multiply the right side:
$x=(-2)(y-2)$
$x=-2y+4$
Interchange $x$ and $y$:
$y=-2x+4$
Substitute $y$ by $f^{1}(x)$:
$f^{-1}(x)=-2x+4$
