Let $f: R \rightarrow R$ be defined by $f(x) = \frac{1}{x}$ for all $x \in R$. Then $f$ is:

Domain of $f(x) = \frac{x}{1-|x|}$ is

The domain of the real valued function $f(x) = \log_{\sqrt{2}}(\sqrt{x^2+x} + \sqrt{x^2-x})$ is

If $f(x) = \frac{2x-3}{(x-2)(x-3)}$ is a real-valued function, then the value that $f(x)$ does not take is:

Let $f:[0,3] \rightarrow A$ be defined by $f(x)=2x^3-15x^2+36x+7$ and $g:[0, \infty) \rightarrow B$ be defined by $g(x)=\frac{x^{2025}}{x^{2025}+1}$. If both the functions are onto and $S =\{ x \in \mathbb{Z} : x \in A \text{ or } x \in B \}$,then $n(S)$ is equal to :

If $f(x) = [x]^{2} - 5[x] + 6 = 0$,where $[x]$ denotes the greatest integer function,then $x \in$