Does it Exist??

Calculus Level 3

Does there exist a continuous function f f defined on the positive reals such that

f ( ∑ k = 0 ∞ x k ∫ 0 1 ( f ( t ) ) k d t ) = − x f\left(\sum _{k=0}^{\infty } \frac{x^k}{\int_0^1 (f(t))^k \, dt}\right)=-x

for all real x x ?

Yes, there are only finitely many such functions (but more than 1) No, no such functions exist Yes, there are infinitely many such functions Yes, there is only one such function

Christopher Criscitiello by Christopher Criscitiello , 25, USA

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