Question

Find the domain of definition of the following function:
$y=\log (5x^2-8x-4)+(x+3{)}^{-0.5}$

Answer 1

For

$\log (5x^2-8x-4)5x^2-8x-4>0(x-2)(5x+2)>0x\in (-\infty ,\frac{-2}{5})\cup (2,\infty )$

and

$x+3>0x>-3$

Taking intersection, we get

$x\in (-3,\frac{-2}{5})\cup (2,\infty )$