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: 64


a) $y=\dfrac{x-8}{4}$; $f(x)=\dfrac{x-8}{4}$ b) $f(3)=-\dfrac{5}{4}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the properties of equality to express the given equation, $ x-4y=8 ,$ 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} x-8=4y \\\\ \dfrac{x-8}{4}=\dfrac{4y}{4} \\\\ y=\dfrac{x-8}{4} .\end{array} Replacing $y$ with $f(x),$ the function notation form of the equation above is \begin{array}{l}\require{cancel} f(x)=\dfrac{x-8}{4} .\end{array} Substituting $x=3,$ in the function above results to \begin{array}{l}\require{cancel} f(3)=\dfrac{3-8}{4} \\\\ f(3)=\dfrac{-5}{4} \\\\ f(3)=-\dfrac{5}{4} .\end{array}
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