Functions

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 \(R\)