Stitz-Zeager_College_Algebra_e-book

It is worth reiterating the importance of nding the

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Unformatted text preview: oots ±3 1.5 Function Notation 47 As long as we substitute numbers other than 3 and −3, the expression r(x) is a real number. Hence, we write our domain in interval notation as (−∞, −3) ∪ (−3, 3) ∪ (3, ∞). When a formula for a function is given, we assume the function is valid for all real numbers which make arithmetic sense when substituted into the formula. This set of numbers is often called the implied domain1 of the function. At this stage, there are only two mathematical sins we need to avoid: division by 0 and extracting even roots of negative numbers. The following example illustrates these concepts. Example 1.5.3. Find the domain2 of the following functions. 1. f (x) = 2 4. r(x) = 4 √ 6− x+3 5. I (x) = 4x 1− x−3 √ 2. g (x) = 4 − 3x √ 3. h(x) = 5 4 − 3x 3x2 x Solution. 1. In the expression for f , there are two denominators. We need to make sure neither of them is 0. To that end, we set each denominator equal to 0 and solve. For the ‘small’ denominator, we get x − 3 = 0 or x = 3. For the...
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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.

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