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I have some confusion in this answer https://math.stackexchange.com/a/2920303/557708

My confusion here see the red markenter image description here

My attempt : $$f(x)= \frac{1}{x} , f^2 = f(f(x) = x , f^3 = f(f(f(x))) = f(x)= \frac{1}{x}$$

Here $f^3= f$ is not integrable but in above answer it said that any power $f^n$ is integrable im confusing How any power $f^n$ is integrable ?

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jasmine
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    They are taking composition, they are raising $f$ to the $n$th power – clark Nov 26 '19 at 21:42
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    I think you're misreading the notation. I believe the exponent is intended to represent exponentiation, not repeated concatenation. In other words, $f^2(x)= f(x) \times f(x)$, not $f(f(x))$. – Robert Shore Nov 26 '19 at 21:43
  • @clark basically in my text book $f^n$ written as composition – jasmine Nov 26 '19 at 21:48
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    @jasmine Yes, but that notation isn't universal. Clearly for the author of the answer $f^2(x)=f(x)\times f(x)$. Note that he explicitly says "the $n$-th power". – Célio Augusto Nov 26 '19 at 21:51

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