Sections 4-1 4-2.pdf - Section 4.1 Inverse functions If a...

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Section 4.1 Inverse functions If a function assigns to each element in a set a unique element in a second set, the inverse does the opposite. In other words given an element in the second set, it will tell us which element was assigned to it from the first. This can easily be understood as a function that does the reverse of another function. Example 1. What would be the inverse of a function that locks a door? The inverse of a function is a function itself. Remember that functions satisfy a vertical line test. When testing to see if a function has an inverse we must first check if it passes a horizontal line test. Functions that do are called one-to-one. Only one-to-one functions have inverses. Example 2. Determine which function is one-to-one and has an inverse. Besides the graph test, one-to-one functions satisfy the following condition: If , then .
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Example 3. Determine whether or not is a one-to-one function.
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