Find the inverse of the function g(x)=(4+3x)/(5-x)

For simplicity first rewrite as y=(4+3x)/(5-x). Now swap any x for a y, and any y for an x. This leaves the equation x=(4+3y)/(5-y). Our goal is to make y the subject of the formula. Multiply both sides by (5-y) to get rid of the denominator on the right hand side of the equation. At this stage we have x(5-y)=(4+3y). Subtract (4+3y) from both sides and expand the x(5-y) term. What we get is 5x-xy-4-3y=0. Collect all the y-terms together to get y(-3-x)+5x-4=0. Now move all the non-y-terms to the right hand side of the equation: y(-3-x)=4-5x Divide through by (-3-x) to obtain y=(4-5x)/(-3-x). Note this can be written as y=(5x+4)/(-1)(3+x). Then we rewrite this as y=-(5x+4)/(3+x) which is the inverse of the original function g(x)=(4+3x)/(5-x).