Can I square both sides of inequality for these functions?

Question

I have two functions $f(x)$ and $g(x)$ for $x>0$. Both functions are monotonically increasing and $f(x)>5$ and $g(x)>0$ .
I know that $f(x)>sqrt{g(x)}$.
Then, can I conclude that $f(x)^2>g(x)$ for $x>0$?

ECL · Answer

Yes, because both $f$ and $sqrt g$ are positive and $zmapsto z^2$ is a strictly increasing function for positive $z$.

Can I square both sides of inequality for these functions?

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