For a real number

MATHEMATICS · Single correct · AoPS · Mathematics · Special Functions · Special Functions

Problem

For a real number

x

, let

[x]

denote the greatest integer less than or equal to

x

. Let

f:\mathbb{R}\to\mathbb{R}

be defined by

f(x)=2x+[x]+\sin x\cos x

. Then

f

is (a) one-one but not onto (b) onto but not one-one (c) both one-one and onto (d) neither one-one nor onto