Let $f , g : \mathbb { N } - \{ 1 \} \rightarrow \mathbb { N }$ be functions defined by $f ( \mathrm { a } ) = \alpha$, where $\alpha$ is the maximum of the powers of those primes $p$ such that $p ^ { \alpha }$ divides $a$, and $g ( a ) = a + 1$, for all $a \in \mathbb { N } - \{ 1 \}$. Then, the function $f + g$ is\\
(1) one-one but not onto\\
(2) onto but not one-one\\
(3) both one-one and onto\\
(4) neither one-one nor onto