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Continuous Function Integral Equation

2175ExpertCalculusFunctions

Olimpiada Republicană la Matematică

Determinați funcțiile continue $f:\left[\frac{1}{e^{2}} ; e^{2}\right] \rightarrow \mathbb{R}$, pentru care $$ \int_{-2}^{2} \frac{1}{\sqrt{1+e^{x}}} f\left(e^{-x}\right) d x-\int_{-2}^{2} f^{2}\left(e^{x}\right) d x=\frac{1}{2} $$
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