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