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A Differentiable Involution.

Source: ISI 2021 P4

July 18, 2021
calculusfunctions

Problem Statement

Let g:(0,∞)→(0,∞)g:(0,\infty) \rightarrow (0,\infty) be a differentiable function whose derivative is continuous, and such that g(g(x))=xg(g(x)) = x for all x>0x> 0. If gg is not the identity function, prove that gg must be strictly decreasing.
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