Inverse functions - by an equation. We use this method to...

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Inverse functions: Basic The one-to-one functions and are defined as follows. Find the following. For a given one-to-one function , there is a related function, , which is the inverse of . The outputs of are inputs of and vice versa. So, if maps to , then maps to . More precisely, if and only if . See Figure 1. We are given the following one-to-one function . Why is it one-to-one? The inverse function reverses the ordered pairs of . Figure 1
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So . We are given the one-to-one function . Why is it one-to-one? There is a general method to find the inverse of a function that is defined
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Unformatted text preview: by an equation. We use this method to find . 1. Replace with . 2. Switch and . 3. Solve for . 4. Finally, replace with . More about these steps To find the value of , we can compute it directly. Because Because But we do not need to do all this work to get . The composition of a function with its inverse always gives an output equal to the input. That is, for any valid input , we have and . More Here is the answer. For additional explanation, see your textbook: Section 2.8: One-to-One Functions and Their Inverses...
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This note was uploaded on 02/10/2009 for the course MATH 107 taught by Professor Self during the Spring '08 term at Washington State University .

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Inverse functions - by an equation. We use this method to...

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