The function $f: R→ [-1,1]$ defined by $f(x) = \cos x$ is:

onto but not one-one

The correct answer is Option (2) → onto but not one-one

The function $f : \mathbb{R} \to [-1, 1]$ defined by $f(x) = \cos x$ is

onto, because $\cos x$ attains all values in $[-1, 1]$ as $x$ varies over $\mathbb{R}$.

Not one-one, because $\cos x$ is periodic and $\cos x = \cos(2\pi + x)$ etc., so multiple $x$ give the same output.