JEE PYQ: Functions Question 8
Question 8 - 2021 (25 Feb Shift 1)
Let $f, g : \mathbb{N} \to \mathbb{N}$ such that $f(n+1) = f(n) + f(a)$ $\forall n \in \mathbb{N}$ and $g$ be any arbitrary function. Which of the following statements is NOT true?
(1) f is one-one
(2) If fog is one-one, then g is one-one
(3) If g is onto, then fog is one-one
(4) If f is onto, then $f(n) = n \ \forall n \in \mathbb{N}$
Type: MCQ
Show Answer
Answer: (3) If g is onto, then fog is one-one
Solution
$f(n) = nf(1)$, so $f(x)$ is one-one. Statement (3) is NOT necessarily true.
BETA
