Question 960733
i believe you mean the inverse graph of f(x) = -3 / (2x-3)


set y = f(x) to get:


y = -3 / (2x-3)


swap y with x to get:


x = -3 / (2y-3)


now you need to solve for y.


multiply both sides of the equation by (2y-3) and divide both sides of the equation by x to get:


2y-3 = -3/x


add 3 to both sides of the equation to get:


2y = 3 - 3/x


divide both sides of the equation by 2 to get:


y = (3 - 3x) / 2


that should be your inverse equation.


if so, then its graph should be a reflection of the original equation of y = -3(2x-3)


your original equation is y = -3 / (2x-3)


your inverse equation is y = (-3/x + 3) / 2


the grpah of your equations is shown below:


<img src = "http://theo.x10hosting.com/2015/040401.jpg" alt="$$$" </>


red is your original equation and blue is your inverse equation.


those equations are reflections about the line y = x.


when the equations are inverse, the  f(x,y) = g(y,x), where f and g are inverse equations of each other.


in the graph, that can be seen by the intersections of the lines y = -x+10 and y = -x + 5 with the respective graphs of the equations that are inverse to each other.


look for the red graph on one side of y = x and the corresponding point of the blue graph on the other side of y = x.