# How do you find the domain of g(x)= root3x/(x^2+x-90)?

Oct 31, 2015

For the domain of x, you need to search the values of x for which this function becomes defined.

One thing, in this function g(x) , it is not defined when the denominator = 0.

So for what value to x does the denominator becomes 0 ?

${x}^{2} + x - 90 = 0$

${x}^{2} + \left(10 - 9\right) - 90 = 0$

${x}^{2} + 10 x - 9 x - 90 = 0$

$x \left(x + 10\right) - 9 \left(x + 10\right) = 0$

$\left(x + 10\right) \left(x - 9\right) = 0$

either,

$x + 10 = 0$
So, $x = - 10$

or,
$x - 9 = 0$
$S o , x = 9$

So when the value of $x$ is either 9 or -10, the denominator becomes 0 and the function g(x) becomes undefined.

Therefore, for all values of $x$ except 9 and -10, the function is defined.

Domain of $x$ is R ( real line ) $\ne$ {9,-10}