Problem 932 (difficulty: 5/10)

Assume that \(\displaystyle f:[0,\infty)\to \R\) is strictly increasing continuous and \(\displaystyle f(0)=0\), \(\displaystyle \lim_{\infty}f=\infty\). Let \(\displaystyle g\) be the inverse function \(\displaystyle f\). Show that

\(\displaystyle xy\leq \int_0^x f \ +\ \int_0^y g.\)

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