Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole

Chapter 1-2 - Cumulative Review - Page 218: 21

Answer

a) $f(3)=-18$ b) $x=11$ c) $\text{Domain: all real numbers} \\\text{Range: all real numbers}$

Work Step by Step

a) To find $f(3),$ substitute $x$ with $3$ in the given function, $f(x)=9x-45.$ Hence, \begin{array}{l}\require{cancel} f(x)=9x-45 \\\\ f(3)=9(3)-45 \\\\ f(3)=27-45 \\\\ f(3)=-18 .\end{array} b) Replace $f(x)$ with $54$ in the given function, $f(x)=9x-45.$ Hence, \begin{array}{l}\require{cancel} f(x)=9x-45 \\\\ 54=9x-45 \\\\ 54+45=9x \\\\ 99=9x \\\\ \dfrac{99}{9}=x \\\\ x=11 .\end{array} c) The domain and the range of linear functions in the form $f(x)=mx+b$ is the set of all real numbers. Hence, the given function has the following characteristics: \begin{array}{l}\require{cancel} \text{Domain: all real numbers} \\\text{Range: all real numbers} .\end{array}

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