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

The range of the function $f(x) = \sqrt{3-x} + \sqrt{2+x}$ is

If $D \subseteq R$ and $f: D \rightarrow R$ defined by $f(x) = \frac{x^2+x+a}{x^2-x+a}$ is a surjection, then '$a$' lies in the interval

Find the set $\{x \in R : \frac{\sqrt{|x|^2-2|x|-8}}{\log(2-x-x^2)} \text{ is a real number}\}$.

The function $f: R \rightarrow R$ is defined by $f(x) = \cos^2 x + \sin^4 x$ for $x \in R$. Then $f(R)$ is equal to:

The domain of definition of $f(x) = \sqrt{\frac{1-|x|}{2-|x|}}$ is: (Here $(a, b) = \{x : a < x < b\}$ and $[a, b] = \{x : a \leq x \leq b\}$)