Ludicrous Limit

Calculus Level 3

The function $$f:\Bbb R^2\to \Bbb R$$ is defined as $f(a,b)=\lim_{x\to\infty}\left(\frac{a^{1/x}+b^{1/x}}2\right)^x$ Find the value of $$f(12, 3)$$.

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