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Question

A function f from the set of natural numbers to integers defined by f(n)={n12,where n is oddn2,where n is even is

A
One-one but not onto
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B
Onto but not one-one
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C
One-one and onto both
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D
Neither one-one nor onto
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Solution

The correct option is C One-one and onto both

f:NI

f(1) = 0, f(2) = -1, f(3) = 1, f(4) = -2, f(5) = 2 and f(6) = -3 so on.

In this type of function every elements of set A has unique image in set B and there is no elements left in set B. Hence f is one - one and onto function.


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