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Precalc0108to0109-page11 - (Section 1.9 Inverses of...

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Unformatted text preview: (Section 1.9: Inverses of One-to-One Functions) 1.9.1 SECTION 1.9: INVERSES OF ONE-TO-ONE FUNCTIONS LEARNING OBJECTIVES • Understand the purposes and properties of inverse functions. • Recognize when a function is one-to-one and invertible, and apply the Horizontal Line Test (HLT) for this purpose. • Know how to find the inverse of a one-to-one function numerically and graphically, and inverse formulas conceptually and mechanically. PART A: DISCUSSION • In Section 1.8, we saw that the graphs of x = y 3 and y = x 3 were the same. Each equation can be solved for the “other variable” to obtain the other equation. We call the corresponding cubing and cube root functions a pair of inverse functions . The graphs of y = x 3 and y = x 3 are reflections about the line y = x . • The term inverse is used in many different contexts. We discussed logical inverses in Section 0.2. We will review additive and multiplicative inverses in this section. Inverse functions are inverses with respect to...
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