Question

Найдите f(x), если известно ,что
$f(x - \frac{2020}{x}) = x { }^{2} + \frac{2020 {}^{2} }{x {}^{2} } - 2021$
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Answer 1

x² + 2020²/x² - 2021 = x² - 2*x*2020/x + 2020²/x² + 2019 = (x - 2020/x)² + 2019

x ≠ 0

f(0) - не определено

f(x - 2020/x) = x² + 2020²/x² - 2021 = (x - 2020/x)² + 2019

x - 2020/x = t

f(t) = t² + 2019

f(x) = x² + 2019