The function $f(x) = \frac{e^{2x} - 1}{e^{2x} + 1}$ is

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

Let $A = \{x \in R : -1 \leq x \leq 1\}$ and $f: A \rightarrow A$ be a mapping defined by $f(x) = x|x|$. Then $f$ is

The function $f: N-\{1\} \rightarrow N$ defined by $f(n) = \text{the highest prime factor of } n$ is:

Are $f$ and $g$ both necessarily onto,if $g \circ f$ is onto?

Let $f: R \rightarrow R$ and $g: R \rightarrow R$ be the functions defined by $f(x) = \frac{x}{1+x^2}$ and $g(x) = \frac{x^2}{1+x^2}$. Then, the correct statement$(s)$ among the following is/are: