2.8 Algebra of Functions and Composition

Miller & Gerken, College Algebra 2e — Pages 298-311

Learning Objectives

Operation	Definition
Sum	\((f + g)(x) = f(x) + g(x)\)
Difference	\((f - g)(x) = f(x) - g(x)\)
Product	\((fg)(x) = f(x) \cdot g(x)\)
Quotient	\(\left(\frac{f}{g}\right)(x) = \frac{f(x)}{g(x)}, \quad g(x) \neq 0\)

Operation

Definition

Sum

\((f + g)(x) = f(x) + g(x)\)

Difference

\((f - g)(x) = f(x) - g(x)\)

Product

\((fg)(x) = f(x) \cdot g(x)\)

Quotient

\(\left(\frac{f}{g}\right)(x) = \frac{f(x)}{g(x)}, \quad g(x) \neq 0\)

\[(f \circ g)(x) = f(g(x))\]

Read as "f of g of x" — apply \(g\) first, then \(f\).

\(x\) must be in domain of \(g\), AND \(g(x)\) must be in domain of \(f\).

Example 1. Example 1

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Problem 1 (p. XX, #YY)

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