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

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Question 1179409: if f(x) = ax+b/cx+d, x≠ -d/c-a/c, find f^-1(x)
Found 2 solutions by Edwin McCravy, greenestamps:
Answer by Edwin McCravy(20059)   (Show Source): You can put this solution on YOUR website!



Write y for f(x)



Interchange x and y



Solve for y:









 

Write f-1(x) for y:

f-1(x) =  

Edwin
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


The other tutor showed a derivation for the answer:

The inverse of is

This particular kind of inverse is encountered often, especially in timed math competitions. While the derivation is not very complicated, it takes time and effort. It might be worthwhile to memorize the answer.

Write the inverse in a slightly different form:

The inverse of is

Note the pattern: The b and c stay where they are; the a and d switch places and switch signs.
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