Is the domain of the following function $\mathbb{R}$?

Question

Is the domain of the following function $\mathbb{R}$?

$$f(x) = \sqrt{1-x} + \sqrt{x-1} $$

Is it a bounded function?

Answer 1

The domain it's just $\{1\}$ because $x\geq1$ and $x\leq1$ gives $x=1$.

Answer 2

We need both $x-1\geq 0$ and $1-x\geq 0$, so $x=1$ is the only point.

Answer 3

The domain is $\{1\}$ and yes it is bounded as $f(1)=0$