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Are any of the following implications always true? Prove or give a counter-example. a) f(n) = (g(n)) -> f(n) = cg(n) + o(g(n)), for some

Are any of the following implications always true? Prove or give a counter-example.

a) f(n) = (g(n)) -> f(n) = cg(n) + o(g(n)), for some real constant c > 0. *(little o in here)

b) f(n) = (g(n)) -> f(n) = cg(n) + O(g(n)), for some real constant c > 0. *(big O in here)

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