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If`f: NvecZf(n)={(n-1)/2,w h e nni sod d-n/2,i d e n t ifyt h ew h e nni se v e n` |
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Answer» Correct Answer - bijective When n is even, let `f(2m_(1))=f(2m_(2))` or `-(2m_(1))/(2)=-(2m_(2))/(2)` or `m_(1)=m_(2)` When n is odd, let `f(2m_(1)+1)=f(2m_(2)+1)` or `(2m_(1)+1-1)/(2)=(2m_(2)+1-1)/(2) " or "m_(1)=m_(2)` Therefore, `f(x)` is one-one. Also, when n is even, `-(n)/(2)=-(2m)/(2)= -m.` When n is odd, `(n-1)/(2)=(2m+1-1)/(2)=m.` Hence, the range of the function is Z. Therefore, function is onto. |
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