Question

The function f : N → N defined by f(x) = x - 5[x/5], where is the set of natural numbers and [x] denotes the greatest integer less than or equal to x, is

(A)  one-one and onto.

(B)  onto but not one-one.

(C)  neither one-one nor onto. 

(D)  one-one but not onto.

Answer 1

Correct  option (C) neither one-one nor onto

The given function is

f(x)  = x - 5[x/5]

Taking x in interval of five natural numbers, we have the following:

Therefore, here, x ∈N. hence, f(x) is neither a one-one function nor onto function.