Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 1 - Functions and Their Graphs - Section 1.1 Functions - 1.1 Assess Your Understanding - Page 55: 81

Answer

$\frac{1}{\sqrt {x+h}+\sqrt x} $

Work Step by Step

Step 1. $f(x+h)=\sqrt {x+h}$ Step 2. $f(x+h)-f(x)=\sqrt {x+h}-\sqrt x$ Step 3. $\frac{f(x+h)-f(x)}{h}=\frac{\sqrt {x+h}-\sqrt x}{h}=\frac{\sqrt {x+h}-\sqrt x}{h}\times\frac{\sqrt {x+h}+\sqrt x}{\sqrt {x+h}+\sqrt x}=\frac{1}{\sqrt {x+h}+\sqrt x} $
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