The range of the function $f(x) = \begin{cases} 4x - 1, & x > 3 \\ x^2 - 2, & -2 \leq x \leq 3 \\ 3x + 4, & x < -2 \end{cases}$ is:

Define the function $f: R \rightarrow R$ by $y = f(x) = x^2, x \in R$. Complete the table given below using this definition. What are the domain and range of this function? Also,draw the graph of $f$.

$x$	$-4$	$-3$	$-2$	$-1$	$0$	$1$	$2$	$3$	$4$
$y = f(x) = x^2$

If the domain of the real valued function $f(x) = \frac{1}{\sqrt{\log_{\frac{1}{3}}\left(\frac{x-1}{2-x}\right)}}$ is $(a, b)$, then $2b =$

If $f(x) = 3 - x^2$ for $1 \le x \le 4$,then the domain of $\log_e(f(2x))$ is:

The range of the function $f(x) = -\sqrt{-x^2-6x-5}$ is

The domain of the function $f(x) = \sqrt{2 - 2x - x^2}$ is