JEE Main 2022 · 27 Jul · Shift 1, Mathematics question 2

Let $f,g:\mathbf N-\{1\}\to\mathbf N$ be functions defined by $f(a)=\alpha$, 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 $a\in\mathbf N-\{1\}$. Then, the function $f+g$ is