Let function 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

As $–∞<2x<∞$ So $–∞<2x+\sin x<∞$ for $x∈R$ $f'(x)=2+\cos x>0$  (always increasing) So f(x) is one-one and onto