# Finding domain of a function

Finding the domain of the function

$$f(x)=\frac{3\sqrt{x}}{x^2-5x-14}$$

My working out

First I factorise the denominator

$$f(x)=\frac{3\sqrt{x}}{(x-7)(x+2)}$$

Therefore the Domain is bigger than 0 and not equal to 7.

$(0,7], [7,\infty)$

Almost, just your notation is off. You mean the domain is $[0,7)\cup (7,\infty)$, to include $0$ in the domain and exclude $7$. – Ian Coley Mar 28 '13 at 0:06
7 is not in the domain, but 0 is, so you should write your answer like this: $[0,7)\cup (7,\infty)$.