Functions Modeling Change: A Preparation for Calculus, 5th Edition

Published by Wiley
ISBN 10: 1118583191
ISBN 13: 978-1-11858-319-7

Chapter 2 - Functions - 2.1 Input and Output - Exercises and Problems for Section 2.1 - Exercises and Problems - Page 75: 4


(a) $g(0)=6$ (b) $x=2,3$

Work Step by Step

(a) To get $g(0)$, use $x=0$ in the expression to get $g(0)=0^2-5(0)+6=6$. (b) Using $g(x)=0$, the following equation is generated: $$x^2-5x+6=0$$Using the quadratic formula $$x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$$ with $a=1$, $b=-5$, and $c=6$, the solutions are $$x=\frac{5 \pm \sqrt{(-5)^2-4(1)(6)}}{2}=\frac{5 \pm \sqrt{25-24}}{2}=\frac{5\pm1}{2}$$ $$x={2,3}$$
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