If a real valued function $f:[-1,2] \rightarrow B$ defined by $f(x) = \begin{cases} 1-x, & -1 \leq x \leq 1 \\ x-1, & 1 < x \leq 2 \end{cases}$ is a surjection,then $B=$

The domain of the function given by $2^x+2^y=2$ is

If the domain of the function $f(x) = \frac{1}{\sqrt{10+3x-x^2}} + \frac{1}{\sqrt{x+|x|}}$ is $(a, b)$,then $(1+a)^2 + b^2$ is equal to :

Domain of $y = \sqrt{\log _{10} \frac{3x - x^2}{2}}$ is

The domain of the function $y = \frac{1}{\sqrt{|x| - x}}$ is

Let $f: A \rightarrow B$ be defined as $f(x) = \frac{1}{2} - \tan \left(\frac{\pi x}{2}\right)$ and $g: B \rightarrow C$ be defined as $g(x) = \sqrt{3 + 4x - 4x^2}$. If $A, B, C$ are subsets of $\mathbb{R}$ and $f$ is an onto function, then the range of the function $f(x)$ is: