The modulus function \(f: R \rightarrow R\), given by \(f(x)=|x|\), is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Neither one-one nor onto
One-one: two different inputs give the same output,
\(f(-1) = |-1| = 1 = f(1)\)
so f is not one-one.
Onto: \(|x| \ge 0\) for every real x, so a negative number such as −1 in the codomain R is not the image of any x. So f is not onto.
Hence f is neither one-one nor onto.
NCERT (2026-27 edition):
Types of Functions
