The function defined by , where N is the set of natural numbers and [x] denotes the greatest integer less than or equal to x, is :
one-one and onto.
one-one but not onto.
onto but not one-one.
neither one-one nor onto.
As we learnt in
Fractional part function -
When Greatest Integer Function
- wherein
Onto function -
If f:AB is such that each & every element in B is the f image of atleast one element in A.Then it is Onto function.
- wherein
The range of f is equal to Co - domain of f.
One - One or Injective function -
A line parallel to x - axis cut the curve at most one point.
-
So that for difference value of x - [x]
lies between 0 and 1 . [0, 6) so that this is not one - one.
Now, y = {x} but so co-domain. So that this is not onto.
Correct option is 4.
Option 1)
one-one and onto.
This is an incorrect option.
Option 2)
one-one but not onto.
This is an incorrect option.
Option 3)
onto but not one-one.
This is an incorrect option.
Option 4)
neither one-one nor onto.
This is the correct option.
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