Question

Find the domain of definition of the following function:
$y=\log \left(\right(x^2-3x\left)\right(x+5\left)\right)$

Answer 1

$y=log\left[\right(x^2-3x\left)\right(x+5\left)\right]$

For $y$ to be real and defined,

${(x}^2-3x\left)\right(x+5)>0x(x-3\left)\right(x+5)>0$

$x(x-3)(x+5)$ is $>0$ between $-5$ and $0$ and after $3$

Therefore, domain of $y$ is $x\in (-5,0)\cup (3,\infty ).$