If $f: R \rightarrow R$,then the function $f(x) = x|x|$ is:

Let $A = \{1, 2, 3, \ldots, n\}$ and $B = \{a, b\}$. If the number of onto functions from $A$ to $B$ is $62$,then the number of subsets of $A$ containing exactly three elements is:

Given below are two statements:
Statement $I$: The function $f:R \rightarrow R$ defined by $f(x) = \frac{x}{1+|x|}$ is one-one.
Statement $II$: The function $f:R \rightarrow R$ defined by $f(x) = \frac{x^{2}+4x-30}{x^{2}-8x+18}$ is many-one.
In the light of the above statements, choose the correct answer from the options given below:

If $f: R \rightarrow R$,such that $f(x)=\frac{e^{x}+e^{-x}}{e^{x}-e^{-x}}$,then $f$ is

The function $f: R \rightarrow R$ defined by $f(x) = e^x + e^{-x}$ is

The function $f: R \to R$ defined by $f(x) = x|x| + x^3|x|$ is