g(x)=\sqrt{x+1/x} I am trying to get the answer for this. What I got is (-inf,+inf). Is this right?
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Which of these functions is it?$\displaystyle g_1 (x) = \sqrt {x + \frac{1}{x}} \,\mbox{ or } \,g_2 (x) = \sqrt {\frac{{x + 1}}{x}} $
The first one.
Originally Posted by Mortifix The first one. Well O.K. $\displaystyle x + \frac{1}{x} = \frac{{x^2 + 1}}{x} \ge 0\quad \Rightarrow \quad x > 0$
Ok so how would I write that in set builder notation. What it be (-inf,0]U[0,inf+)?
Originally Posted by Mortifix Ok so how would I write that in set builder notation. What it be (-inf,0]U[0,inf+)? $\displaystyle \left\{ {x \in \mathbb{R}:x > 0} \right\} = \left( 0 \right.,\left. \infty \right)$
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