Find-f-x-such-that-f-2x-f-x-

Question Number 132932 by bobhans last updated on 17/Feb/21

F i n d f (x) s u c h t h a t f (2 x) = f (x)

Answered by Olaf last updated on 17/Feb/21

f (2 x) = f (x)

\Rightarrow f (x) = f (\frac{x}{2}) = f (\frac{x}{4}) = \dots f (\frac{x}{2^{n}}) \dots

f (x) = \lim_{n \to \infty} f (\frac{x}{2^{n}}) = f (0) = constant

If f (0) exists, f is a constant function

and f (x) = f (0)

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