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Functional square root

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In mathematics, a functional square root is a square root of a function with respect to the operation of function composition. In other words, the functional square root of a function g is a function f satisfying f(f(x)) = g(x) for all x. For example, f(x) = 2x2 is a functional square root of g(x) = 8x4.

The functional square root of the exponential function was studied by Hellmuth Kneser in 1950.

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