JEE PYQ: Functions Question 34
Question 34 - 2019 (10 Jan Shift 2)
Let $\mathbb{N}$ be the set of natural numbers and two functions $f$ and $g$ be defined as $f, g : \mathbb{N} \to \mathbb{N}$ such that $f(n) = \begin{cases} \frac{n+1}{2} & \text{if } n \text{ is odd} \ \frac{n}{2} & \text{if } n \text{ is even} \end{cases}$ and $g(n) = n - (-1)^n$. Then $f \circ g$ is:
(1) onto but not one-one
(2) one-one but not onto
(3) both one-one and onto
(4) neither one-one nor onto
Type: MCQ
Show Answer
Answer: (1) onto but not one-one
Solution
$f(g(1)) = f(g(2)) = 1$, $f(g(3)) = f(g(4)) = 2$, etc.
$f \circ g$ is onto but not one-one.
BETA
