The domain of the function $f: R \rightarrow R$ defined by $f(x) = \sqrt{x^{2}-7x+12}$ is

The range of the function $f(x) = \frac{x^2+x+1}{x^2-x+1}$ is

If $f: R \rightarrow R$ is defined by $f(x)=[2x]-2[x]$ for $x \in R$,where $[x]$ is the greatest integer not exceeding $x$,then the range of $f$ is:

If $[x]$ represents the greatest integer $\leq x$ and $[\alpha, \beta]$ is the set of all real values of $x$ for which the real function $f(x)=\frac{\sqrt{3+x}+\sqrt{3-x}}{\sqrt{[x]+2}}$ is defined,then $f^2(\alpha+1)+5 f^2(\beta)=$

Given $f(x) = \frac{1}{2} - \tan^{-1}\left(\frac{\pi x}{2}\right)$ for $-1 < x < 1$ and $g(x) = \sqrt{3 + 4x - 4x^2}$. Find the domain of $(f + g)$.

Define the real-valued function $f: R - \{0\} \rightarrow R$ defined by $f(x) = \frac{1}{x}$,where $x \in R - \{0\}$. Complete the table given below using this definition. What is the domain and range of this function?

$x$	$-2$	$-1.5$	$-1$	$-0.5$	$0.25$	$0.5$	$1$	$1.5$	$2$
$y = \frac{1}{x}$	....	....	....	....	....	....	....	....	....