Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 1 - Section 1.2 - Basics of Functions and Their Graphs - Exercise Set - Page 176: 29


(a) $g(-1)=2$ (b) $g(x+5)= x^2+12x+38$ (c) $g(-x)=x^2-2x+3$

Work Step by Step

RECALL: $g(a)$ represents the value of the function $g$ when $x=a$. Evaluate the function by substituting the given value of $x$. (a) Substitute $4$ into $x$ to obtain: $g(-1) = (-1)^2+2(-1)+3 \\g(-1)=1+(-2)+3 \\g(-1)=-1+3 \\g(-1)=2$ (b) Substitute $x+5$ into $x$ to obtain: $g(x+5) = (x+5)^2+2(x+5)+3 \\g(x+5)= x^2+10x+25+2x+10+3 \\g(x+5)= x^2+12x+38$ (c) Substitute $-x$ into $x$ to obtain: $g(-x) = (-x)^2+2(-x)+3 \\g(-x) = x^2+(-2x)+3 \\g(-x)=x^2-2x+3$
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