If $[a, b]$ is the range of the function $f(x) = \frac{x+2}{2x^2+3x+6}$ for $x \in \mathbb{R}$,then:

Domain of the real valued function $f(x) = \frac{x+2}{9-x^{2}}$ is

Let $f$ be a function such that $f(x) = \sum_{r=1}^n [r + \cos(\frac{x}{r})]$,where $[.]$ denotes the greatest integer function and $x \in [0, \pi]$. Then the range of $f(x)$ is:

Given that $a, b$ and $c$ are real numbers such that $b^2 = 4ac$ and $a > 0$. The maximal possible set $D \subseteq R$ on which the function $f: D \rightarrow R$ given by $f(x) = \log \{ax^3 + (a+b)x^2 + (b+c)x + c\}$ is defined,is

The domain of the function $f(x) = \sqrt{\log_e\left(\frac{1}{x^2-4x+4}\right)} + \sin^{-1}(x^2-2)$ is

If $f: R \rightarrow R$ is defined as $f(x) = \frac{x^6}{x^6+2020}$,for all $x \in R$,then the range of $f$ is .......