SOLUTION: If f(x) = ax+b/cx+d, x ≠ -d/c, -a/c, find f^-1(x)

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Question 1180066: If f(x) = ax+b/cx+d, x ≠ -d/c, -a/c, find f^-1(x)
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Take the given function

y=%28ax%2Bb%29%2F%28cx%2Bd%29

To find the inverse, switch the x and y...

x+=+%28ay%2Bb%29%2F%28cy%2Bd%29

...and solve for the new y.

I leave it to you to do that.

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:

The inverse of the function

y=%28ax%2Bb%29%2F%28cx%2Bd%29

is

y=%28-dx%2Bb%29%2F%28cx-a%29

Note in the inverse function, compared to the original...

the "b" and "c" coefficients remain in the same places, unchanged; and
the "a" and "d" coefficients switch places and change sign.

So of course if you solve for the new y algebraically, as suggested above, your answer should be

y=%28-dx%2Bb%29%2F%28cx-a%29