Answer
$f(x)=\frac{5x-3}{2x-1}$
Work Step by Step
Step 1: Switch $f(x)$ or $y$ and $x$ in the original function.
$x=\frac{y-3}{2y+5}$
Multiply both sides by the denominator to cancel out the denominator.
$2xy-5x = y-3$
Add $5x$, then subtract $y$.
$2xy-y=5x-3$
Factor out y.
$y(2x-1)=5x-3$
Divide by $2x-1$.
$y=\frac{5x-3}{2x-1}$
or
$f(x)=\frac{5x-3}{2x-1}$