Stitz-Zeager_College_Algebra_e-book

To nd a sign diagram for g we look for the zeros of g

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Unformatted text preview: unction inverses are unique.2 Suppose g and h are both inverses of a function f . By Theorem 5.2, the domain of g is equal to the domain of h, since both are the range of f . This means the identity function I2 applies both to the domain of h and the domain of g . Thus h = h ◦ I2 = h ◦ (f ◦ g ) = (h ◦ f ) ◦ g = I1 ◦ g = g , as required.3 We summarize the discussion of the last two paragraphs in the following theorem.4 Theorem 5.3. Uniqueness of Inverse Functions and Their Graphs : Suppose f is an invertible function. • There is exactly one inverse function for f , denoted f −1 (read f -inverse) • The graph of y = f −1 (x) is the reflection of the graph of y = f (x) across the line y = x. The notation f −1 is an unfortunate choice since you’ve been programmed since Elementary Algebra 1 to think of this as f . This is most definitely not the case since, for instance, f (x) = 3x + 4 has as 1 its inverse f −1 (x) = x−4 , which is certainly different than f (x) = 3x1 . Why does this confusing 3 +4...
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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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