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Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.

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Regions when a concave function is smaller than another concave function

Let $f_1,f_2:[0,1]\mapsto\mathbb{R}$ be two bounded and concave functions. Assume $f_1(0)<f_2(0)$ and $f_1(1)<f_2(1)$. I want to investigate the set $\mathcal{X}\triangleq\{x\in[0,1]: f_1(x)>f_2(x)\}$ …
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