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If f(n)=O(g(n))  for f,g are non decreasing functions ,then

f(n)*log2(f(n)c) =O(g(n) * log2g(n)) , c is power of f(n) is

a)Always true

b) Never

c) Sometimes true , sometimes not depending on f,g

d) Sometimes true, sometimes false depending on c

1 Answer

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f(n) * log2(f(n)c) = O (g(n) * log2g(n)) 

=> c * f(n) * log2(f(n)) = O (g(n) * log2g(n)) 

=>  f(n) * log2(f(n)) = O (g(n) * log2g(n)) 

Even we can check if it is always true or not,

A). 1/n2 = O(1/n)  --> True in this ( f,g are non decreasing functions, so, i should not include this example, but even if we use , it is true )

B). n = O(n2) --> Even true for this .

Answer:

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