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A function f from the set of natural num...

A function f from the set of natural number to integers defined by
`f(n)={{:(,(n-1)/(2),"when n is odd"),(,-(n)/(2),"when n is even"):}`

Text Solution

Verified by Experts

Clearly f(6) = 3 and f(5) = 3
Hence `5 != 6` but f(5) = f(6)
Therefore, f is not one-one
Clearly, for every `m in N`, there exists `2m-1 in N`
such that `f(2m-1) = m`
Hence f is onto.
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