Range of the function $f(x) = \sin^2(x^4) + \cos^2(x^4)$ is

Find the range of the function $f(x)$ defined by:
$f(x) = \begin{cases} 2x-3, & x < -1 \\ 1-x^2, & -1 \leq x \leq 1 \\ 3x^2+2, & x > 1 \end{cases}$

The set of all real values of $x$ such that $f(x) = \sqrt{\frac{[x]-1}{[x]^2-[x]-6}}$ is a real-valued function is

If the range of $f(x) = \frac{2x^4-14x^2-8x+49}{x^4-7x^2-4x+23}$ is $(a, b]$,then $(a + b)$ is

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

$A$ real-valued function $f: A \rightarrow B$ defined by $f(x) = \frac{4-x^2}{4+x^2}$ for all $x \in A$ is a bijection. If $-4 \in A$,then $A \cap B =$