# 1.7 - 1.7 Combinations of Functions Composite Functions 1...

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1.7 Combinations of Functions; Composite Functions 1. Find the domain of a function. To find the domain of a function defined by an equation: 1. Start with the domain as the set of real numbers. 2. If the equation has a denominator, exclude any numbers that give a zero denominator. 3. If the equation has a radical of even index, exclude any numbers that cause the expression inside the radical to be negative. Note: When the domain is not specified, in this class we assume that the domain is the set of all real numbers that, as inputs, produce real number outputs . Example: Find the domain of 11 () 23 fx xx   .

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2. Combine functions using the algebra of functions, specifying domains. The domain of f+g is the set of all real numbers that are common to the domain of f and the domain of g. Thus we must find the domains of f and g before finding their intersection. The domain of f g is the set of all real numbers that

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1.7 - 1.7 Combinations of Functions Composite Functions 1...

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