Precalculus Functions and Graphs
Inverse Functions Concepts 1

|  |  | Definition |  |
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Let f be a one-to-one function with domain D and range R. The inverse of f is a function f -1 with domain R and range D for which: f( f -1(x))= x for every x in R and f -1(f(x))=x for every x in D.

|  |  | Statement 1 |  |
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Finding f -1 To find f -1 for one-to-one function f: Write y instead of f(x); Interchange x and y; Solve the equation x = f(y) for y; Write f -1(x) instead of y.

Example. Given: f(x) = 3x+2. Find: formula for f -1(x).
Solution

1. | y | = | 3x+2 |  | Write y instead of f(x).
2. | x | = | 3y+2 |  | Interchange x and y.
3. | 3y+2 | = | x |  | Solve the equation x = f(y) for y.
| 3y | = | x-2 |  |
| y | = |  |  |
4. | f-1(x) | = |  |  | Write f -1(x) instead of y.

|  |  | Statement 2 |  |
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The graph of an inverse function can be obtained by reflecting the graph of the original function in the line y=x.

|  | f(x) = 3x+2

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