Domain of the function $\sqrt{\log \left\{ \frac{5x - x^2}{6} \right\}}$ is

The range of the function $f(x) = x^2 + \frac{1}{x^2+1}$ is

If $f:[-3,2] \rightarrow [0, \sqrt[3]{x}]$ is an onto function defined by $f(n) = \begin{cases} 2+\sqrt[3]{n}, & -3 \leq n \leq -1 \\ n^{2/3}, & -1 < n \leq 2 \end{cases}$, then $x=$

If $f(x)$ is a real function defined on $[-1, 1]$, then the function $g(x) = f(5x + 4)$ is defined on the interval

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 definition of the function $y(x)$ given by $2^x + 2^y = 2$ is