Inverses
Finding Inverses
In an earlier discussion about finding inverses, three different methods were discussed. One way is to switch x and y in the equation and solve for y. However, because of the multiple terms and powers of a polynomial, this process can be difficult to do. Graphing the polynomial and using the horizontal line test is a fairly easy method to determine if a polynomial's inverse is a function.
If the graph does not pass the horizontal line test, the polynomial will not have an inverse that is a function so there will not be a need to graph it. If the horizontal line test determines the polynomial function has an inverse function, graph the inverse by following the steps below:
Step 1. Identify several points (x, y) on the graph of the given function.
Step 2. Switch the x- and y-coordinates of each point to form the points (y, x) for the inverse function.
Step 3. Plot the new points and connect them with a smooth curve.
The graph of the inverse should be a reflection of the polynomial's graph across the y = x line.