Stitz-Zeager_College_Algebra_e-book

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

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

## 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.

Ask a homework question - tutors are online