## College Algebra 7th Edition

$f^{-1}(x)=\frac{5x+3}{1-2x}$
We are given: $f(x)=\displaystyle \frac{x-3}{2x+5}$ To find the inverse of $f$, we switch $x$ and $y$ and solve for $y$: $y= \frac{x-3}{2x+5}$ $x= \frac{y-3}{2y+5}$ $x(2y+5)=y-3$ $2xy+5x=y-3$ $5x+3=y-2xy$ $5x+3=y(1-2x)$ $y=\frac{5x+3}{1-2x}$ Therefore, the inverse is: $f^{-1}(x)=\frac{5x+3}{1-2x}$