suppose F(n)=2logn and G(n)=logn here f(n)=O(g(n))
but
2f(n)=22logn
2g(n)=2logn now assume 2logn=x
then 2f(n)= x2
and 2g(n)=x
so 2f(n)=O(2g(n)) is not hold
this was expalnation ??
For Option 1 below link might be helpful
https://math.stackexchange.com/questions/819186/fn-thetafn-2-prove-or-disprove