Stitz-Zeager_College_Algebra_e-book

Stitz-Zeager_College_Algebra_e-book

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Unformatted text preview: piciously like some kind of distributive property, it is nothing of the sort; the addition on the left hand side of the equation is function addition, and we are using this equation to define the output of the new function f + g as the sum of the real number outputs from f and g .1 Example 1.6.1. Let f (x) = 6x2 − 2x and g (x) = 3 − 1 . Find and simplify expressions for x 1. (f + g )(x) 3. (f g )(x) 2. (g − f )(x) 4. 1 g f (x) The author is well aware that this point is pedantic, and lost on most readers. 56 Relations and Functions In addition, find the domain of each of these functions. Solution. 1. (f + g )(x) is defined to be f (x) + g (x). To that end, we get (f + g )(x) = f (x) + g (x) = 6x2 − 2x + 3 − 1 x 1 x 6x3 2x2 3x 1 − + − x x x x 3 − 2x2 + 3x − 1 6x x = 6 x2 − 2x + 3 − = = get common denominators To find the domain of (f + g ) we do so before we simplify, that is, at the step 6x2 − 2x + 3 − 1 x We see x = 0, but everything else is fine. Hence, the domain is (−∞, 0) ∪ (0, ∞). 2. (g...
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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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