The domain of $f(x) = \log \left[(2.5)^{3-x^2} - (0.4)^{x+9}\right]$ is

Range of the function $\frac{1}{2 - \sin 3x}$ is

Find the domain and the range of the real function $f$ defined by $f(x) = \sqrt{x-1}$.

If $[x]^2-5[x]+6=0$,where $[\cdot]$ denotes the greatest integer function,then $x$ belongs to:

The sum of the least positive integer and the greatest negative integer in the range of the function $f(x) = \frac{x^2-5x+7}{x^2-5x-7}$ 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 :