Find the domain of the function $f(x) = \frac{x^{2}+3x+5}{x^{2}-5x+4}$.

For $f(x) = \frac{\sin \pi[x]}{1+[x]} + \frac{x}{2+3x}$,where $[x]$ denotes the greatest integer function,the domain and range in $R$ are respectively

If $R$ is the set of all real numbers and $f: R-\{2\} \rightarrow R$ is defined by $f(x)=\frac{2+x}{2-x}$ for $x \in R-\{2\}$, find the range of $f(x)$.

$\left\{x \in R: \frac{2 x-1}{x^3+4 x^2+3 x} \in R\right\}$ equals

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 :

The domain of the function $f(x) = \log |\log x|$ is: