f x 3x12x3 find f1x and the domin and rangeSolutionfx3x12x3

f (x) = 3x+1/2x-3 find f^-1(x) and the domin and range

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

domain:

2x-30

x3/2

x=(-infinity,3/2)U(3/2,infinity)

range; y3/2

y=(-infinity,3/2)U(3/2,infinity)

let y =f(x)

x=f ^-1(y)

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

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

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

2xy-3x =1+3y

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

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

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

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