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# L03 - Lecture 3 Inverse Functions Purpose of inverse...

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Lecture 3 — Inverse Functions Purpose of inverse functions A function f is one-to-one (1–1) if Horizontal Line Test: If no horizontal line passes through a graph in more than one point, then Show the function f ( x ) = x 3 is (1–1) in two ways. Increasing functions and decreasing functions are

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Suppose that f is a (1–1) function. Then it has a unique inverse function f - 1 that assigns to each x in the range of f the unique value of y that solves f ( y ) = x . That is, f - 1 ( x ) = y if and only if f ( y ) = x . Thus, graphically: ( x,y ) is on the graph of f - 1 if and only if and the graph of f - 1 is the graph of f reﬂected across What then must be the domain/range of f - 1 ?
Pairs of inverse functions are unique in that they ”undo” one another—that is: f - 1 ( f ( x ) ) = f ( f - 1 ( x ) ) = Demonstrate that f ( x ) = x 3 + 1 and g ( x ) = 3 x - 1 are a pair of inverse functions. Note that you have been using inverse functions

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L03 - Lecture 3 Inverse Functions Purpose of inverse...

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