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# L12 - Lecture 12 Section 1.9 Inverse Functions Def If a...

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Lecture 12: Section 1.9 Inverse Functions Def. If a function u1D453 is a set of ordered pairs ( u1D465,u1D466 ), then inverse relation of u1D453 is the set of ordered pairs ( u1D466,u1D465 ). ex. Find the inverse relation of the following func- tions. Is the inverse a function? 1) u1D453 : { ( 2 , 2) , (3 , 1) , (4 , 0) , ( 1 , 2) } 2) u1D454 : { ( 2 , 2) , (3 , 1) , (0 , 0) , (4 , 1) } NOTE: An inverse of a function may not be a function.

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One-to-One Functions Def. A function u1D453 is a one-to-one function if each value of the dependent variable ( u1D466 ) corresponds to exactly one value of the independent variable ( u1D465 ). That is, given any two elements u1D465 1 and u1D465 2 in the domain of u1D453 , if u1D465 1 = u1D465 2 , then u1D453 ( u1D465 1 ) = u1D453 ( u1D465 2 ). NOTE: If a function u1D453 is a set of ordered pairs, u1D453 is one-to-one if no two ordered pairs have the same second element. An inverse of a function u1D453 is also a function if and only if u1D453 is a one-to-one function. ex. Let u1D453 ( u1D465 ) = u1D465 2 . Is u1D453 a one-to-one function?
Horizontal Line Test A function u1D453

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L12 - Lecture 12 Section 1.9 Inverse Functions Def If a...

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