Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 1 - Section 1.2 - Basics of Functions and Their Graphs - Exercise Set - Page 180: 126


The value of the given expression is\[\frac{f\left( a+h \right)-\left( a \right)}{h}=3\]

Work Step by Step

Calculate the function value for $x=a+h$ and for $x=a$ $\begin{align} & f\left( x \right)=3x+7 \\ & f\left( a+h \right)=3\left( a+h \right)+7 \\ & f\left( a \right)=3a+7 \end{align}$ Now, substitute these values in the given expression to calculate its value $\begin{align} & \frac{f\left( a+h \right)-\left( a \right)}{h}=\frac{3\left( a+h \right)+7-\left( 3a+7 \right)}{h} \\ & =\frac{3a+3h+7-3a-7}{h} \\ & =\frac{3h}{h} \\ & =3 \end{align}$ Thus, the value of the expression is $\frac{f\left( a+h \right)-\left( a \right)}{h}=3$.
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