# Thread: Finding the domain of a function

1. ## Finding the domain of a function

g(x)=\sqrt{x+1/x}

I am trying to get the answer for this. What I got is (-inf,+inf). Is this right?

2. Which of these functions is it? $
g_1 (x) = \sqrt {x + \frac{1}{x}} \,\mbox{ or } \,g_2 (x) = \sqrt {\frac{{x + 1}}{x}}$

3. The first one.

4. Originally Posted by Mortifix
The first one.
Well O.K.
$x + \frac{1}{x} = \frac{{x^2 + 1}}{x} \ge 0\quad \Rightarrow \quad x > 0$

5. Ok so how would I write that in set builder notation. What it be (-inf,0]U[0,inf+)?

6. Originally Posted by Mortifix
Ok so how would I write that in set builder notation. What it be (-inf,0]U[0,inf+)?
$\left\{ {x \in \mathbb{R}:x > 0} \right\} = \left( 0 \right.,\left. \infty \right)$