Find the inverse of fx 3x2 2x1 Be sure to state the domain

Find the inverse of f(x) = (3x-2) / (2x+1). Be sure to state the domaine of f^-1(x)

Solution

f(x) = (3x-2) / (2x+1)

let f(x)=y

=>x=f ^-1(y)

(3x-2) / (2x+1)=y

(3x-2) =(2x+1)y

3x-2 =2xy +y

3x- 2xy =2+y

x(3-2y)=(2+y)

x=(2+y)/(3-2y)

f ^-1(y) =(2+y)/(3-2y)

f ^-1(x) =(2+x)/(3-2x)

domaine of f^-1(x) is (-infinity,3/2)U(3/2,infinity)