## Algebra and Trigonometry 10th Edition

Published by Cengage Learning

# Chapter 2 - 2.2 - Functions - 2.2 Exercises - Page 183: 52

#### Answer

$(-\infty,0)\cup(0,4)\cup(4,\infty)$

#### Work Step by Step

We are given the function: $h(x)=\dfrac{6}{x^2-4x}$ Factor the denominator: $h(x)=\dfrac{6}{x(x-4)}$ The domain of the function contains all real numbers $x$ except the zeros of the denominator. Determine the zeros of the denominator: $x(x-4)=0$ $x=0$ or $x-4=0$ $x=0$ or $x=4$ The domain is: $(-\infty,0)\cup(0,4)\cup(4,\infty)$

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