0 0 0 2 y f x y f x near x 2 2 in

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Unformatted text preview: r a proof of this, we refer the reader to Example 1.1.6 in Section 1.1 and Exercise 14 in Section 2.1. A plot of the inverse functions f (x) = 3x + 4 and g (x) = x−4 confirms this. 3 y 2 y = f (x) y=x 1 x −2 −1 1 2 −1 y = g (x) −2 If we abstract one step further, we can express the sentiment in Definition 5.2 by saying that f and g are inverses if and only if g ◦ f = I1 and f ◦ g = I2 where I1 is the identity function restricted1 to the domain of f and I2 is the identity function restricted to the domain of g . In other words, I1 (x) = x for all x in the domain of f and I2 (x) = x for all x in the domain of g . Using this description of inverses along with the properties of function composition listed in Theorem 5.1, 1 The identity function I , which was introduced in Section 2.1 and mentioned in Theorem 5.1, has a domain of all real numbers. In general, the domains of f and g are not all real numbers, which necessitates the restrictions listed here. 5.2 Inverse Functions 295 we can show that f...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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