Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 6 - Radical Functions and Rational Exponents - Chapter Test - Page 427: 18

Answer

$-2g(x) + f(x) = -2x^2 + 7x - 6$ $\text{The domain is all real numbers.}$

Work Step by Step

In this problem, we are asked to add two functions. Let us go ahead and set up the addition problem, separating the two functions with parentheses: $-2g(x) + f(x) = -2(x^2 - 3x + 2) + (x - 2)$ Use distributive property to remove the parentheses, but pay attention to the operation in front of the parentheses: $-2g(x) + f(x) = -2x^2 + 6x - 4 + x - 2$ Group like terms: $-2g(x) + f(x) = -2x^2 + (6x + x) + (- 4 - 2)$ Combine like terms: $-2g(x) + f(x) = -2x^2 + 7x - 6$ There are no restrictions on the variable. The domain is all real numbers since no value of $x$ will make the expression/function undefined.
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