Determine all real continuous functions $f$ such that $f^2(x) = -x$.
2026-04-06 07:35:53.1775460953
Possible functions satisying $f^2(x) = -x$.
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I belive you have misread this question. Obviuosly there is no continuous function $f: \mathbb R \to v$ such that $(f(x))(f(x))=-x$ for all, $x$ because LHS is non-negative. I think the person who asked this question wanted you to interpret the equation as $f(f(x))=-x$ for all $x$. Actually there is no continuous function satisfying this last condition: it is obvious that $f$ is one-to-one. Since it is continuous it is strictly monotonic. But then $f\circ f$ is strictly increasing but $-x$ is decreasing so the given equation cannot hold.