Question 1
Find all continuous $f:[e^{-2},e^2]\to\mathbb R$ satisfying
$$\int_{-2}^2\frac{f(e^{-x})}{\sqrt{1+e^x}}\,dx-\int_{-2}^2f(e^x)^2\,dx=\frac12.$$
$$\int_{-2}^2\frac{f(e^{-x})}{\sqrt{1+e^x}}\,dx-\int_{-2}^2f(e^x)^2\,dx=\frac12.$$
MathNet 2020 — Math Olympiad Vault — Part 05 Question 1
Math Olympiad Vault · MathNet 2020 — Math Olympiad Vault — Part 05