Find the inverse of the function

Question

f(x) =3/(2x-4)

Answer 1

f(x) =3/(2x-4)

y =3/(2x-4)

Switch x and y

x=3/(2y-4)

Multiply each side by (2y-4)

x(2y-4) =[3/(2y-4)](2y-4)

x(2y-4) =3

Divide each side by x

x(2y-4) =3

(2y-4) =(3/x)

Add 4 to each side

(2y-4)+4 =(3/x)+4

2y=(3/x)+4

divide each side by 2

y=[(3/x)+4]/2

  =[(3/x)]/2+[4/2]

  =(3/(2x))+2

Switch x and y

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

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