Answer
$f^{-1}(x)=\frac{x-3}{2}$
The graphs of $f$ (blue line) and $f^{-1}$ (red line) are shown in the following image:
Work Step by Step
Equation given:
$f(x)=2x+3$
Replace $f(x)$ with $y$:
$y=2x+3$
Make $x$ the subject:
$\frac{y-3}{2}=x$
Interchange $y$ with $x$:
$y=\frac{x-3}{2}$
Replace $y$ with $f^{-1}(x)$:
$f^{-1}(x)=\frac{x-3}{2}$
Graph $f$ and $f^{-1}$ using technology or by making a table of ordered pairs for each line and joining the points found.