Algebra and Trigonometry, 5th Edition

Chapter 5 Summary and Review

Study Guide

KEY TERMS AND CONCEPTS	EXAMPLES
SECTION 5.1: INVERSE FUNCTIONS
Inverse Relation If a relation is defined by an equation, then interchanging the variables produces an equation of the inverse relation.	Given $y=-5x+7$, find an equation of the inverse relation. $$\begin{array}{rcll}y& =& -5x+7& \mathbf{\text{Relation}}\\ \downarrow & \downarrow \\ x& =& -5y+7& \mathbf{\text{Inverse relation}}\end{array}$$
One-to-One Functions A function f is one-to-one if different inputs have different outputs—that is, $$\mathrm{if}a\ne b,\mathrm{then}f(a)\ne f(b).$$ Or a function f is one-to-one if when the outputs are the same, the inputs are the same—that is, $$\mathrm{if}f(a)=f(b),\mathrm{then}a=b.$$	Prove that $f(x)=16-3x$ is one-to-one. Show that if $f(a)=f(b)$, then $a=b$. Assume $f(a)=f(b)$. Since $f(a)=16-3a$ and $f(b)=16-3b$, $$\begin{array}{rcl}16-3a& =& 16-3b\\ -3a& =& -3b\\ a& =& b.\end{array}$$