Given f(x) = (2x)/(x+3), how do you find f^(-1) (4)?

1 Answer
Aug 7, 2015

I found: f^-1(4)=-6

Explanation:

I start rearranging the original function y=f(x)=(2x)/(x+3) solving it for x to get:
(x+3)*y=2x
xy+3y-2x=0
xy-2x=-3y
x(y-2)=-3y
and:
x=f(y)=(-3y)/(y-2) or changing x with y you get:
f^-1(x)=(-3x)/(x-2)
and
f^-1(4)=(-3*4)/(4-2)=-12/2=-6