find the inverse of f(x)=(6x)/(x+1)

Question

i dont know how to get rid of the second y

Answer 1

Let f(x) = y:   y = 6x/(x+1)

 

Switch x and y:  x = 6y/(y+1)

 

Solve for y:  x(y+1) = 6y

 

                  xy + x = 6y

 

                  xy - 6y = -x

 

                    y(x-6) = -x

 

                          y = -x/(x-6) = x / (6-x) = f^-1(x)