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Q. 16

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Found in: Page 225

### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465

# Find the domain of the rational function. $G\left(x\right)=\frac{6}{\left(x+3\right)\left(4-x\right)}$

The domain of the given function is $\left(-\infty , -3\right)\cup \left(-3, 4\right)\cup \left(4, \infty \right)$

See the step by step solution

## Step 1. Given information

The given function is $G\left(x\right)=\frac{6}{\left(x+3\right)\left(4-x\right)}$

## Step 2. Find the domain

For the domain, the denominator should not be equal to zero.

So,

$\left(x+3\right)\left(4-x\right)\ne 0\phantom{\rule{0ex}{0ex}}x+3\ne 0\phantom{\rule{0ex}{0ex}}x\ne -3\phantom{\rule{0ex}{0ex}}or\phantom{\rule{0ex}{0ex}}4-x\ne 0\phantom{\rule{0ex}{0ex}}x\ne 4$

Thus, the domain of the given function is all real numbers except $-3$ and $4$.

Therefore, the domain is $\left(-\infty , -3\right)\cup \left(-3, 4\right)\cup \left(4, \infty \right)$