Question

If f(x) = (x+1) / (x-2), find the inverse of f(x) ?

Answer 1

Refer to explanation

Explanation:

The domain of f(x) is `R-{2}` and the inverse is

#f(x)=(x-1)/(x+2)=>y=(x-1)/(x+2)=>y*(x+2)=x-1=> y*x+2y=x-1=>2y+1=x-yx=>x=(2y+1)/(1-y)# hence we have that

`f^(-1)(x)=(2x+1)/(1-x)`