Answer
$f^{-1}(x)=\frac{x-3}{5x+2}$
Work Step by Step
Let $f(x)=y$.
Then,
$y=\frac{2x+3}{1-5x}$ (Cross Multiply)
$y(1-5x)=2x+3$ (Distribute $y$)
$y-5xy=2x+3$ (Move $y$ and $2x$ and change their signs)
$-5xy-2x=-y+3$ (Factor ou $x$)
$x(-5y-2)=-y+3$ (Divide by $-5y-2$)
$x=\frac{-y+3}{-5y-2}$ (Use the property $y=f(x)\Leftrightarrow x=f^{-1}(y)$)
$f^{-1}(y)=\frac{-y+3}{-5y-2}$
Thus, the inverse function of $f(x)$ is $f^{-1}(x)=\frac{x-3}{5x+2}$.
