College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 2 - Section 2.3 - Functions - 2.3 Exercises - Page 201: 65

Answer

a) $y=-2x^2-x+3 $; $f(x)=-2x^2-x+3$ b) $f(3)=-18$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the properties of equality to express the given equation, $ y+2x^2=3-x ,$ in terms of $y.$ Then replace $y$ with $f(x),$ to express the answer in function notation form. Finaly, substitute $x=3,$ to find $f(3).$ $\bf{\text{Solution Details:}}$ Using the properties of equality, the given equation is equivalent to \begin{array}{l}\require{cancel} y=-2x^2-x+3 .\end{array} Replacing $y$ with $f(x),$ the function notation form of the equation above is \begin{array}{l}\require{cancel} f(x)=-2x^2-x+3 .\end{array} Substituting $x=3,$ in the function above results to \begin{array}{l}\require{cancel} f(3)=-2(3)^2-(3)+3 \\\\ f(3)=-2(9)-3+3 \\\\ f(3)=-18-3+3 \\\\ f(3)=-18 .\end{array}
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