Question

Let f : R →R be a function defined by f(x) = [x]2 + [x + 1] – 3 {where [.] denontes greatest integer function}, then f(x) is

(A) many-one

(B) onto

(C) one-one

(D) into

Answer 1

Correct Option:- (A) (D)

Explanation :-

f(x) = [x]2 + [x] – 2

Let [x] = t

f(t) = t2 + t – 2 = (t + 2) (t – 1)

so f(x) is may - one into