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Let f :R→Rf\colon\mathbb R \to \mathbb R f:R→R be a continuous function satisfying f(x)+∫0xtf(t) dt+x2=0\displaystyle f(x) + \int_0^x t f(t) \, dt + x^2 = 0 f(x)+∫0xtf(t)dt+x2=0 for all real xxx.
Which of the following is true?
Source: KVPY 2015 (SX/SB stream).
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