devarshi-dt-logo

Question:

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

one-one but not onto

one-one and onto

onto but not one-one

neither one-one nor onto

Solution:

f(x) = x-[x/5]
Take x in intervals of 5 natural numbers
f(x) = { 0 0 ≤ x < 5
{ 1 5 ≤ x < 10
{ 2 10 ≤ x < 15
{ 3 15 ≤ x < 20
x ∈ N.
From the graph, we can see that f(x) is neither one-one nor onto (as it does not take all N).