MathDB

4

Part of 2021 ISI Entrance Examination

Problems(1)

A Differentiable Involution.

Source: ISI 2021 P4

7/18/2021
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.
calculusfunctions