If $f:[2,3] \rightarrow R$ is defined by $f(x)=x^3+3x-2$,then the range of $f(x)$ is contained in the interval

The domain of definition of the function $f(x) = \sqrt{1 + \log_{e}(1 - x)}$ is

The domain of definition of the function $f(x) = \frac{3}{4 - x^2} + \log_{10}(x^3 - x)$ is

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:

If $[x]^2-5[x]+6=0$,where $[x]$ denotes the greatest integer function,then

Let $f(x)=\sqrt{2-x-x^2}$ and $g(x)=\cos x$. Which of the following statements are true?
$I$. Domain of $f((g(x))^2) = \text{Domain of } f(g(x))$
$II$. Domain of $f(g(x)) + g(f(x)) = \text{Domain of } g(f(x))$
$III$. Domain of $f(g(x)) = \text{Domain of } g(f(x))$
$IV$. Domain of $g((f(x))^3) = \text{Domain of } f(g(x))$