Question

Determine the domain of the function.

Answer 1

$\left\{\begin{array}{ccc}x+4\geq0&(1)\\(x+2)(x-5)\neq0&(2)\end{array}\right\\\\(1)\ x+4\geq0\ \ \ |-4\\x\geq-4\to x\in\left\ \textless \ -4;\ \infty\right)\\\\(2)\ (x+2)(x-5)\neq0\iff x+2\neq0\ \wedge\ x-5\neq0\\\\x\neq-2\ \wedge\ x\neq5\\\\\text{The domain:}\\\\x\geq-4\ \wedge\ x\neq-2\ \wedge\ x\neq5\\\\x\in\left\ \textless \ -4;\ -2\right)\ \cup\ (-2;\ 5)\ \cup\ (5;\ \infty)$