Graph y = 3x to the second power - 5 and its inverse

You can see graph of the function  in the first picture. Now to find its inverse, we are going to switch  and  in our function, and then solve for 





Remember that every time that you take a square root, you will have tow results: one positive and one negative. Therefore, our function  will have tow inverses:  and .
In the first picture you can see the graph of the original function; in the second one the graphs of its inverses, and in the third one all the graphs together. Notice that our original function is a quadratic function, and quadratic functions don't have inverse functions unless their domains are restricted.