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: 68

Answer

a) $y=\dfrac{2x+9}{5}$; $f(x)=\dfrac{2x+9}{5}$ b) $f(3)=3$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the properties of equality to express the given equation, $ -2x+5y=9 ,$ 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} 5y=2x+9 \\\\ y=\dfrac{2x+9}{5} .\end{array} Replacing $y$ with $f(x),$ the function notation form of the equation above is \begin{array}{l}\require{cancel} f(x)=\dfrac{2x+9}{5} .\end{array} Substituting $x=3,$ in the function above results to \begin{array}{l}\require{cancel} f(3)=\dfrac{2(3)+9}{5} \\\\ f(3)=\dfrac{6+9}{5} \\\\ f(3)=\dfrac{15}{5} \\\\ f(3)=3 .\end{array}
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.