Which of the following functions is a monotonically increasing function?

In the interval $(7, \infty)$,the function $f(x) = |x-5| + 2|x-7|$ is:

The real valued function $f(x) = \frac{x^2}{2} - \log(x^2 + x + 1)$ 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 $R$.

The function $f(x) = (1/2)^x$ on $R$ is

The function $f(x) = 1 - x^3 - x^5$ is decreasing for