I'm being asked to evaluate if $f(n)$ is a member of $\theta(g(n))$.
$() =(4 × )^{150} + (2 × + 1024)^{400}\,$ vs. $\,() = 20 × ^{400} + {( + 1024)}^{200}$
From what I understand, we should ignore the constants and focus on the highest power in both equations, so in this case it would evaluate to $f(n) = {n}^{400}$ and $g(n) = {n}^{400}$, which means we can find constants $c_1$ and $c_2$ that will satisfy the condition and conclude that $f(n)$ is a member of $g(n)$.
But I don't think this is right.
When we consider the formula $0 \le c_1 \cdot g(n) \le f(n) \le c_2\cdot g(n)-$ should we consider only the highest orders or take into consideration the whole function?
Confused and would like some clarity, thanks!