# How do you find the domain of the function in interval notation for g(x)= sqrtx/(x^2+x-90)?

Apr 7, 2015

$g \left(x\right) = \frac{\sqrt{x}}{{x}^{2} + x - 90}$
= sqrt(x)/((x+10)(x-9)

Restrictions based by the numerator
$x \ge 0$

Restrictions place by denominator
$x \ne - 10$ (this is eliminated by the restriction of the numerator)
and $x \ne 9$

In interval notation
Domain of $g \left(x\right) = \left\{\left[0 , 9\right) , \left(9 , + \infty\right]\right\}$