Answer
$f^{-1} (x)= \dfrac{4-5x}{2(2x-3)}=\dfrac{4-5x}{4x-6}$
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 $y$.
$x=\dfrac{6y+4}{4y+5} \implies x(4y+5)=6y+4$
or, $4xy-6y=4-5x$
or, $2y(2x-3)=4-5x \implies y= \dfrac{4-5x}{2(2x-3)}$
Replace $y$ with $f^{-1} (x)$.
so, $f^{-1} (x)= \dfrac{4-5x}{2(2x-3)}=\dfrac{4-5x}{4x-6}$
