# If f(x)= 2 -x^(1/2) and g(x)= x^2- 9, what is the domain of g(x)div f(x)?

Sep 23, 2017

$f \left(x\right) = \left(2 - {x}^{\frac{1}{2}}\right)$ and $g \left(x\right) = {x}^{2} - 9$

so, $g \left(x\right) \div f \left(x\right) = \frac{{x}^{2} - 9}{2 - {x}^{\frac{1}{2}}}$

Now, the denominator cannot be zero

i.e. $2 - {x}^{\frac{1}{2}} \ne 0$

so, ${x}^{\frac{1}{2}} \ne 2$

Hence, $x \ne 4$

Therefore, the domain is all values except $x = 4$

:)>