First thing you do when you're looking for an inverse is to switch the x and the y coordinates. That is done in the 6th box down. [tex]x= \frac{3y}{8+y} [/tex]. Next we are going to multiply both sides by 8+y to get rid of the denominator. That is done in the 1st box: x(8+y)=3y. Then we will distribute the x into the parenthesis, which is done in the last box: 8x+xy=3y. Next we will move the xy term over by subtraction to the other side, which is done in the 3rd box down: 8x=3y-xy. Now we will factor a y out of the right side, which is done in the 4th box down: 8x=y(3-x). In order to isolate the y term, we will divide both sides by 3-x, which is the 2nd box down AND your inverse: [tex] f^{-1}(x)=y= \frac{8x}{3-x} [/tex]. And there you go!
