A relation \(f: \mathrm{N} \to \mathrm{N}\) be defined by \(f(x) = x^2, x \in \mathrm{N}\) (Set of Natural numbers), then \(f(x)\) is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → injective only
Injective (one-one): let \(f(x_1) = f(x_2)\) for natural numbers \(x_1, x_2\).
\(x_1^2 = x_2^2\)
\(x_1 = x_2\) (both are positive)
So f is injective.
Surjective (onto): the images \(f(x) = x^2\) are only the perfect squares 1, 4, 9, 16, …. The natural number 2 is not a perfect square, so no x in N has \(f(x) = 2\).
So f is not surjective, and f is injective only.
NCERT (2026-27 edition):
Types of Functions
