Answer
$f^{-1} (x)= \dfrac{-5x-3}{(2x-5)}=\dfrac{-(5x+3)}{(2x-5)}$
Work Step by Step
When we apply the horizontal test, it has been noticed that the function is one-to-one and verifies the horizontal test.
Therefore, the function has an inverse function.
To compute the inverse, we will have to interchange $x$ and $y$.
$x=\dfrac{5y-3}{2y+5} \implies 2xy-5y=-5x-3$
or, $y(2x-5)=-5x-3 \implies y= \dfrac{-5x-3}{(2x-5)}$
Replace $y$ with $f^{-1} (x)$.
so, $f^{-1} (x)= \dfrac{-5x-3}{(2x-5)}=\dfrac{-(5x+3)}{(2x-5)}$
