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: 66


a) $y=3x^2+x+2$; $f(x)=3x^2+x+2$ b) $f(3)=32$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the properties of equality to express the given equation, $ y-3x^2=2+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=3x^2+x+2 .\end{array} Replacing $y$ with $f(x),$ the function notation form of the equation above is \begin{array}{l}\require{cancel} f(x)=3x^2+x+2 .\end{array} Substituting $x=3,$ in the function above results to \begin{array}{l}\require{cancel} f(3)=3(3)^2+3+2 \\\\ f(3)=3(9)+3+2 \\\\ f(3)=27+3+2 \\\\ f(3)=32 .\end{array}
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