If you’re asked to graph the inverse of a function, you can do so by remembering one fact: a function and its inverse are reflected over the line y = x. This line passes through the origin and has a slope of 1.

When you’re asked to draw a function and its inverse, you may choose to draw this line in as a dotted line; this way, it acts like a big mirror, and you can literally see the points of the function reflecting over the line to become the inverse function points. Reflecting over that line switches the x and the y and gives you a graphical way to find the inverse without plotting tons of points.

To see how x and y switch places, follow these steps:

Take a number (any that you want) and plug it into the first given function.
Say you pick –4. When you evaluate f(–4), you get –11. As a point, this is written (–4, –11).
Take the value from Step 1 and plug it into the other function
In this case, you need to find g(–11). When you do, you get –4 back again. As a point, this is (–11, –4).

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2 years ago