Let f : R → R be defined by f(x) = 2x + sin x for x ∈ R. Then f is :

one to one and onto one to one but not onto onto but not one to one neither one to one nor onto

one to one and onto

f’(x) = 2 + cos x > ∀ x Hence f(x) is always increasing, hence it will be one-one. Range is R. Hence f will be onto. Hence (1) is the correct answer.