If the domain of the function $f(x) = x^2 - 6x + 7$ is $(-\infty, \infty)$,then the range of the function is

The range of $f(x) = \sec \left( \frac{\pi }{4} \cos^2 x \right)$ for $-\infty < x < \infty$ is

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

Find the range of the following function:
$f(x) = 2 - 3x$,where $x \in R$ and $x > 0$.

Is it true that $x = e^{\log x}$ for all real $x$?

Let the sets $A$ and $B$ denote the domain and range respectively of the function $f(x)=\frac{1}{\sqrt{\lceil x\rceil-x}}$ where $\lceil x \rceil$ denotes the smallest integer greater than or equal to $x$. Then among the statements
$(S1): A \cap B = (1, \infty) - \mathbb{N}$ and
$(S2): A \cup B = (1, \infty)$