Answer
$f^{-1}(x)=\dfrac{x-3}{5x+2}$
Work Step by Step
$f(x)=\dfrac{2x+3}{1-5x}$
Rewrite this expression as $y=\dfrac{2x+3}{1-5x}$ and solve for $x$:
$y=\dfrac{2x+3}{1-5x}$
Take $1-5x$ to multiply the left side:
$y(1-5x)=2x+3$
$y-5xy=2x+3$
Take $2x$ to the left side and $y$ to the right side:
$-5xy-2x=3-y$
Take out common factor $x$ from the left side:
$x(-5y-2)=3-y$
Take $-5y-2$ to divide the right side:
$x=\dfrac{3-y}{-5y-2}$
$x=\dfrac{y-3}{5y+2}$
Interchange $x$ and $y$:
$y=\dfrac{x-3}{5x+2}$
The inverse of the original function is $f^{-1}(x)=\dfrac{x-3}{5x+2}$
