In which interval is the function $f(x) = x^x$ a decreasing function?

In the interval $[0, 1]$,the function $f(x) = x^2 - x + 1$ is

Which statement among the following is true?
$(i)$ The function $f(x) = x|x|$ is strictly increasing on $R - \{0\}$.
$(ii)$ The function $f(x) = \log_{(1/4)} x$ is strictly increasing on $(0, \infty)$.
$(iii)$ $A$ one-one function is always an increasing function.
$(iv)$ $f(x) = x^{1/3}$ is strictly decreasing on $R$.

If $f(x) = \begin{cases} 0, & x = 0 \\ x - 3, & x > 0 \end{cases}$,then $f(x)$ is:

Let $R^* = R - \left\{ (2k - 1) \frac{\pi}{2} \mid k \in I \right\}$. The function $f: R^* \rightarrow R$ is defined as $f(x) = \tan x - x$, then $f(x)$ is

If $a < 0$,then the function $f(x) = e^{ax} + e^{-ax}$ is monotonically decreasing for all values of $x$ where ...