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Example: Finding the Inverse of the Function {(0,3),(1,5),(2,7),(3,9)}
Find the inverse of the function {(0, 3), (1, 5), (2, 7), (3, 9)} and determine the domain and range of the inverse.
First, confirm that the function is one-to-one: every -value is paired with exactly one -value, and no -value is repeated.
To find the inverse, reverse the - and -values in each ordered pair:
| Ordered Pairs | |
|---|---|
| Function | {(0, 3), (1, 5), (2, 7), (3, 9)} |
| Inverse Function | {(3, 0), (5, 1), (7, 2), (9, 3)} |
The domain of the inverse function is the set of all its -values: {3, 5, 7, 9}. The range of the inverse function is the set of all its -values: {0, 1, 2, 3}.
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Intermediate Algebra @ OpenStax
Ch.10 Exponential and Logarithmic Functions - Intermediate Algebra @ OpenStax
Algebra
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