Answer:
Sadly, I cannot sketch this inverse for you, but I can help try to explain what to do when you see problems like this.
How to Sketch the Inverse:
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).
