The domain of definition of function f(x)=log x2-5x-24  -x-2,is

# The domain of definition of function is

1. A

$\left(-\infty ,-3\right]$

2. B

$\left(-\infty ,-3\right]\cup \left[8,\infty \right)$

3. C

$\left(-\infty ,\frac{-28}{9}\right)$

4. D

None of these

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### Solution:

Here,
$\sqrt{{\mathrm{x}}^{2}-5\mathrm{x}-24}>\mathrm{x}+2$ is equivalent to the collection of two system of inequations.
Case I

Case II

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