Find Inverse of a Function

Question

Find inverse of: f(x)= x

------

x-3

y

x= --- (divide both sides by y-3)

y-3

xy-3x = y Am I correct so far? How would I complete this process?

Answer 1

Nearly right

y = x / (x-3)

xy - 3y = x

xy - x - 3y = 0

x (y-1) - 3y = 0

x = 3y / (y-1)

Switch x and y

y = 3x / (x-1)

This is your inverse function

f^-1(x) = 3x / (x-1)

f^-1 f (x) should be x , by definition of inverse function

This is (3x/x-3 ) / (x/x-3 - 1) = (3x/x-3) / ( 3/ x-3) = x as required

Answer 2

you are correct so far, now put all the y's on one side of the equation and factor:

xy-y=3x, y(x-1)=3x, y=3x/(x-1)