Answer
$f^{-1}(x)=-\dfrac{x+3}{2}$
Work Step by Step
The expression $f(x)=-2x+3$ is equivalent to $y=-2x+3$. Interchanging the $x$ and $y$ variables, and then solving for $y$, then the inverse is
\begin{array}{l}
x=-2y+3\\
2y=-x+3\\
y=-\dfrac{x+3}{2}\\
.\end{array}
Hence, the inverse is $
f^{-1}(x)=-\dfrac{x+3}{2}
.$
