We are given 2 algorithms A and B such that for each input size, algorithm A performs half the number of steps algorithm B performs on the same input size.
We denote the worst time complexity of each one by $g_A(n),g_B(n)$
Also, we know there's a positive function $f(n)$ such that $g_A(n)\in\Omega(f(n))$
Is it possible that $g_B(n)\in\Omega(f(n))$? Is it necessary?
It seems naive to think that it's necessary, but I can't figure out to contradict it.