Show that if f(x) is a real-valued, continuous function on the half-line 0≤x<∞, and ∫0∞f2(x)dx<∞ then the function g(x)\equal{}f(x)\minus{}2e^{\minus{}x}\int_0^x e^tf(t)dt satisfies \int _0^{\infty}g^2(x)dx\equal{}\int_0^{\infty}f^2(x)dx. [B. Szokefalvi-Nagy] functionintegrationreal analysisinequalitieslimitreal analysis unsolved