The function \(f: \mathrm{R} \rightarrow \mathrm{R}, f(x) = |x|\) (\(\mathrm{R}\) is the set of real numbers) is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → neither injective nor surjective
f is injective (one-one) only if different inputs always give different outputs. But
\(f(-2) = |-2| = 2 = f(2)\)
with \(-2 \ne 2\), so f is not injective.
f is surjective (onto) only if every real number is an output. But \(|x| \ge 0\) for all x, so the range is \([0, \infty)\), and a negative number such as −1 has no pre-image. So f is not surjective.
Hence f is neither injective nor surjective.
NCERT (2026-27 edition):
Types of Functions
