Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 2 - Section 2.6 - Function Notation and Linear Functions - 2.6 Exercises - Page 203: 52


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

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the properties of equality to isolate $y$ in the given equation, $ -2x+5y=9 ,$ and then express in function notation. Then find $f(3)$ by substituting $x$ with $3.$ $\bf{\text{Solution Details:}}$ Using the properties of equality, the given equation is equivalent to \begin{array}{l}\require{cancel} -2x+5y=9 \\\\ 5y=2x+9 \\\\ \dfrac{5y}{5}=\dfrac{2x}{5}+\dfrac{9}{5} \\\\ y=\dfrac{2}{5}x+\dfrac{9}{5} .\end{array} Using $y=f(x),$ the function notation of the equation above is $ f(x)=\dfrac{2}{5}x+\dfrac{9}{5} .$ Substituting $x$ with $ 3 ,$ then \begin{array}{l}\require{cancel} f(x)=\dfrac{2}{5}x+\dfrac{9}{5} \\\\ f(3)=\dfrac{2}{5}(3)+\dfrac{9}{5} \\\\ f(3)=\dfrac{6}{5}+\dfrac{9}{5} \\\\ f(3)=\dfrac{15}{5} \\\\ f(3)=3 .\end{array} Hence, \begin{array}{l}\require{cancel} \text{a) } f(x)=\dfrac{2}{5}x+\dfrac{9}{5} \\\\\text{b) } f(3)=3 .\end{array}
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