Finding the closest possible $\Omega$, $\mathcal{O}$ - bound (or if possible $\Theta$) for the following functions

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So I have three functions:

$f(n) = n^{2/12} + log^{2018}(n)$

$g(n) = n^{2+(-1)^n}$

$h(n) = n(1+(-1)^n)$

I think for $f$ it would be $f(n)$ $\in$ $\Theta(n^{2/12})$, because $n^{2/12}$ grows faster than $log^{2018}(n)$, so $log^{2018}(n)$ is a constant factor.

But what about g and h? Arent they both alternating between $\infty$ and $-\infty$. Are there even a $\Omega$, $\mathcal{O}$ or $\Theta$ - bounds for them?