Find the domain of the function $f(x) = \frac{x^{2}+2x+1}{x^{2}-8x+12}$.

The function is defined as $f(x) = (1 + \frac{1}{x})^x$. What is the range of the function $f(x)$?

If the equation $\frac{1}{x} + \frac{1}{x - 1} + \frac{1}{x - 2} = 3x^3$ has $k$ real roots,then $k$ is equal to -

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:

The range of the function $f : R \rightarrow R$,defined by $f(x) = \frac{(x + 1)^4}{x^4 + 1}$,is

If $[x]$ denotes the greatest integer $\leq x$, then the domain of the function $f(x)=\sqrt{\frac{4-x^2}{[x]+2}}$ is