Evaluating a Function and Its Inverse from a Graph at Specific Points

A function $g (x)$ is given in Figure 5. Find $g (3)$ and $g^{- 1} (3) .$

Figure 5

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
To evaluate $g (3),$ we find 3 on the x-axis and find the corresponding output value on the y-axis. The point $(3, 1)$ tells us that $g (3) = 1.$
To evaluate $g^{- 1} (3),$ recall that by definition $g^{- 1} (3)$ means the value of x for which $g (x) = 3.$ By looking for the output value 3 on the vertical axis, we find the point $(5, 3)$ on the graph, which means $g (5) = 3,$ so by definition, $g^{- 1} (3) = 5.$ See Figure 6.

Figure 6

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Using the graph in Figure 6, ⓐ find $g^{- 1} (1),$ and ⓑ estimate $g^{- 1} (4) .$

How did it go?