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: 49

Answer

$\text{a) } f(x)=-2x^2+3 \\\\\text{b) } f(3)=-15$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the properties of equality to isolate $y$ in the given equation, $ y+2x^2=3 ,$ 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} y+2x^2=3 \\\\ y=-2x^2+3 .\end{array} Using $y=f(x),$ the function notation of the equation above is $ f(x)=-2x^2+3 .$ Substituting $x$ with $ 3 ,$ then \begin{array}{l}\require{cancel} f(x)=-2x^2+3 \\\\ f(3)=-2(3)^2+3 \\\\ f(3)=-2(9)+3 \\\\ f(3)=-18+3 \\\\ f(3)=-15 .\end{array} Hence, \begin{array}{l}\require{cancel} \text{a) } f(x)=-2x^2+3 \\\\\text{b) } f(3)=-15 .\end{array}
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