## Algebra and Trigonometry 10th Edition

$f^{-1} (x)= \dfrac{4-5x}{2(2x-3)}=\dfrac{4-5x}{4x-6}$
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, $f^{-1} (x)= \dfrac{4-5x}{2(2x-3)}=\dfrac{4-5x}{4x-6}$