Let N be the set of natural numbers and two functions f and g be defined as f, g : N $ \to $ N such that f(n) = $$\left\{ {\matrix{ {{{n + 1} \over 2};} & {if\,\,n\,\,is\,\,odd} \cr {{n \over 2};} & {if\,\,n\,\,is\,\,even} \cr } \,\,} \right.$$; and g(n) = n $-$($-$ 1)n. Then fog is -

Question

Let N be the set of natural numbers and two functions f and g be defined as f, g : N $ \to $ N such that

f(n) = $$\left\{ {\matrix{ {{{n + 1} \over 2};} & {if\,\,n\,\,is\,\,odd} \cr {{n \over 2};} & {if\,\,n\,\,is\,\,even} \cr } \,\,} \right.$$;

and g(n) = n $-$($-$ 1)ⁿ.

Then fog is -

neither one-one nor onto

onto but not one-one

both one-one and onto

one-one but not onto

Solution

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