SOLUTION: Describe the constant a and b such that f(x)= (2x+a)/(bx-2) and f(x)=f^-1(x) for all x in the domain of f.

Algebra ->  Functions -> SOLUTION: Describe the constant a and b such that f(x)= (2x+a)/(bx-2) and f(x)=f^-1(x) for all x in the domain of f.       Log On


   

Question 1048296: Describe the constant a and b such that
f(x)= (2x+a)/(bx-2) and f(x)=f^-1(x) for all x in the domain of f.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=++%282x%2Ba%29%2F%28bx-2%29
===>
===> x%28bf%5E%28-1%29%28x%29-2%29+=++%282f%5E%28-1%29%28x%29%2Ba%29
===> f%5E%28-1%29%28x%29+=+%282x%2Ba%29%2F%28bx-2%29, after some more algebraic manipulations.
===> f%28x%29+=+f%5E%28-1%29%28x%29 , for all x common to their domains.
===> There are no restrictions on the values a and b.