Let \(f: \mathrm{R} \rightarrow \mathrm{R}\) be a function defined as \(f(x) = x^4\). Which one of the following is true?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(f\) is neither one-one nor onto.
One-one: f is not one-one, because two different inputs give the same output:
\(f(1) = 1 = f(-1)\), but \(1 \ne -1\)
Onto: f is not onto, because \(x^4 \ge 0\) for every real x, so a negative number in the codomain R, such as −1, has no pre-image:
\(x^4 = -1\) has no real solution.
NCERT (2026-27 edition):
Types of Functions
