The function \(f: \mathrm{R} \rightarrow [-1, 1]\) defined by \(f(x) = \cos x\) is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → onto but not one-one
Onto: as x runs over all real numbers, cos x takes every value in \([-1, 1]\), and \([-1, 1]\) is the whole codomain. So f is onto.
Not one-one: different inputs give the same output, for example
\( f(0) = \cos 0 = 1 \)
\( f(2\pi) = \cos 2\pi = 1 \)
So f is onto but not one-one.