JEE Main2003MathematicsFunctionsActual

A function f from the set of natural numbers to integers defined by f ( n )= array l n -1 2 , when n isodd n 2 , when n is even array . is

Options

Aneither one-one nor onto
Bone-one but not onto
Conto but not one-one
Done-one and onto both.

Correct answer

D. one-one and onto both.

Step-by-step solution

f: N 1f(1)=0, f(2)=-1, f(3)=-1, f(4)=-2f(5)=2 , and f(6)=-3 so on. In this type of function every element of set A has unique image in set B and there is no element left in set B . Hence f is one-one and onto function.

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