Question 1180066
<br>
Take the given function<br>
{{{y=(ax+b)/(cx+d)}}}<br>
To find the inverse, switch the x and y...<br>
{{{x = (ay+b)/(cy+d)}}}<br>
...and solve for the new y.<br>
I leave it to you to do that.<br>
This is a common type of problem, usually using numerical coefficients instead of a, b, c, and d, on high school math competitions.  There is a quick shortcut that is easily memorized to make this kind of problem easy to solve quickly:<br>
The inverse of the function<br>
{{{y=(ax+b)/(cx+d)}}}<br>
is<br>
{{{y=(-dx+b)/(cx-a)}}}<br>
Note in the inverse function, compared to the original...<br>
the "b" and "c" coefficients remain in the same places, unchanged; and
the "a" and "d" coefficients switch places and change sign.<br>
So of course if you solve for the new y algebraically, as suggested above, your answer should be<br>
{{{y=(-dx+b)/(cx-a)}}}<br>