Question

Find the inverse of the function f(x) =3x/(x-2)

Answer 1

The function is f(x)  =  3x / (x - 2).

Find the inverse of the function.

Change y  =   3x / (x - 2).

Interchange x and y.

x  =   3y / (y - 2).

Solve for y.

x (y - 2)  =   3y

xy - 2x  =  3y

xy - 3y  =  2x

y(x - 3)  =  2x

y  =  2x / (x - 3)

Change y to f^-1 (x).

f^-1 (x)  =  2x / (x - 3) ,  [ x not equal to 3 ]

Answer :

f^-1 (x)  =  2x / (x - 3)