Question on Finding the Value of Inverse Function

Topic : Inverse Function

Question : Find the inverse of the Function f(x)=(4x-1)/(3x+2)

Solution :
Let g be the inverse of function f then,
f(g(x)) = x So,
4g(x)-1
--------- = x
3g(x)+2
For convinience, lets write only g instead of g(x)
So 4g-1 / 3g+2 = x
4g-1=x(3g+2)
4g-1=3gx+2x
Subtract 3gx on both sides
4g-3gx-1 = 2x
add 1 from both sides
4g-3gx = 2x +1
g(4-3x) = 2x+1
g=2x+1 / (4-3x)
or g = - (2x+1) / (3x+4)
and inverse of f(x) is - (2x+1) / (3x+4)