JEE MAIN - Mathematics (2017 - 9th April Morning Slot - No. 7)
The function f : N $$ \to $$ N defined by f (x) = x $$-$$ 5 $$\left[ {{x \over 5}} \right],$$ 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.
Explanation
f(1) = 1 - 5$$\left[ {{1 \over 5}} \right]$$ = 1
f(6) = 6 - 5$$\left[ {{6 \over 5}} \right]$$ = 1
So, this function is many to one.
f(10) = 10 - 5$$\left[ {{10 \over 5}} \right]$$ = 0 which is not present in the set of natural numbers.
So this function is neither one-one nor onto.
f(6) = 6 - 5$$\left[ {{6 \over 5}} \right]$$ = 1
So, this function is many to one.
f(10) = 10 - 5$$\left[ {{10 \over 5}} \right]$$ = 0 which is not present in the set of natural numbers.
So this function is neither one-one nor onto.
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