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Question

A graph of a function f is given.

Does f have an inverse?

YesNo    

If so, find the following. (If an answer does not exist, enter DNE.)

f −1(−1)	=
f −1(2)	=

Answer 1

Yes, it has an inverse. To find the inverse of a graph, just flip it over (reflect it over) the y=x line (the diagonal) so that the positive x-axis turns into the positive y-axis and visa-versa. The inverse would look like the blue graph:

To find f^-1(-1) find what value of "x" results in f(x) being equal to -1. That would be x = 2. So for f(x), the point (2, -1) is on the graph. For the inverse function (-1, 2) will be on the graph. So f^-1(-1) = 2

Since f(5) = 2, then f^-1(2) = 5