## Calculus (3rd Edition)

Published by W. H. Freeman

# Chapter 1 - Precalculus Review - 1.3 The Basic Classes of Functions - Exercises - Page 23: 40

#### Answer

$c\in(-2,2)$

#### Work Step by Step

We are given the function: $f(x)=\dfrac{x+1}{x^2+2cx+4}$ The function has domain $\mathbb{R}$ if the denominator is not zero.therefore it doesn't have real zeros. Determine the values of $c$ for which the denominator is not zero: $(2c)^2-4(1)(4)<0$ $4c^2-16<0$ $4(c^2-4)<0$ $c^2-4<0$ $c\in(-2,2)$

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