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

f^-1 is the inverse of f(x)

 

(2x+3)/(x-4)   = y       solve for 'x'

first do the division on the left to get

2+ 11/(x-4) = y          subtract 2 from each side

11/(x-4) = y-2          re-arrange

11/(y-2) = x-4          add 4 to both sides

11/(y-2) + 4 = x       change y to x and x to y

11/(x-2) +4 = y        simplify

 

(11 + 4x -8 )/(x-2) = y

(4x+3) / (x-2) = f^-1