Find the domain of $g(t)=\sqrt{\frac{t}{2}-\frac{1}{t}}$

Question

$$g(t) = \sqrt{\frac{t}{2} - \frac{1}{t}}$$

Case 1: $t/2 - 1/t \geq 0$ ; $t \geq 2$

Case 2: $t$ cannot equal $0$

Is this correct? Thank you.

Answer 1

You definitely want 2 criteria, but they are not independent cases:

1. $t\ne 0$
2. $t/2 - 1/t \ge 0 \iff t/2 \ge 1/t$

In the second case, it will help to distinguish between $t>0$ and $t<0$. Can you finish it?