#### Answer

The domain of $x$ is $x\geq 1$.

#### Work Step by Step

From trigonometric identity we have $\sec^2 t-\tan^2 t=1$. Since $x=\sec t$ and $y=\tan t$, we obtain $x^2-y^2=1$. So,
$y=\pm \sqrt{x^2-1}$.
For the interval $0\leq t1$. Hence, the domain of $x$ is $x\geq 1$.