2.8.A.1Concept
On a specified domain, a function, f, has an inverse function, or is invertible, if each output value of f is mapped from a unique input value. The domain of a function may be restricted in many ways to make the function invertible.
ExampleCheck a table1 / 3
Which of the two functions is invertible? If one is not, restrict its domain so that it is.
| x | 1 | 2 | 3 | 4 | 5 |
| f(x) | 4 | 7 | 1 | 9 | 6 |
| x | 1 | 2 | 3 | 4 | |
| g(x) | 3 | 5 | 3 | 8 |
Try it on paper first, then reveal each step to check your work.
Step 1 — Look at f
The outputs 4, 7, 1, 9, 6 are all different. Each output comes from one input, so f is invertible.