The function $f(x) = \operatorname{sech}(x)$ on $R$ has the range

Find the range of the function $f(x)$ defined by:
$f(x) = \begin{cases} 2x-3, & x < -1 \\ 1-x^2, & -1 \leq x \leq 1 \\ 3x^2+2, & x > 1 \end{cases}$

Find the domain and the range of the real function $f$ defined by $f(x) = |x - 1|$.

For the function $f(x) = (1 + \frac{1}{x})^x$,the domain of $f(x)$ is:

If function $f : R \to S, f(x) = (\sin x - \sqrt{3} \cos x + 1)$ is onto,then $S$ is equal to

The domain of the real-valued function $f(x) = \frac{\sqrt{\log_{10}\left(\frac{x}{x-2}\right)}}{\sqrt{[x]^2-5[x]+6}}$ is (where $[x]$ denotes the greatest integer function):