JEE Main 2022 (Online) 27th July Morning ShiftQuestion 1
Let $f,g:\mathbb{N}-\{1\}\to\mathbb{N}$ 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 $a\in\mathbb{N}-\{1\}$. Then, the function $f+g$ is
Sets, Relations and Function
Solution
$h(a)=f(a)+a+1$. $h(4)=2+5=7$ and $h(5)=1+6=7$, so $h$ is not one-one. $h(a)\ge1+3=4$ for all $a\ge2$, so $1\notin$ range: not onto. Neither: option D.