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**Supplementary question to "interesting problem" post**

If f(2x)=f(f(x))

and f(2x+1)=f(2x)+1

then for what value n such that n is in the set of natural numbers could f(0) equal 2^n.

also for what value n does f(0) equal 2^n +2?

- Thread starter jdp
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- #1

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If f(2x)=f(f(x))

and f(2x+1)=f(2x)+1

then for what value n such that n is in the set of natural numbers could f(0) equal 2^n.

also for what value n does f(0) equal 2^n +2?

- #2

Bacle2

Science Advisor

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You get : f(0)=f(f(0))

f(1)=f(0)+1

Use x=-1/2 , then f(-1)=f(f(-1/2)

f(0)=f(-1)+1

for x=-1 , f(-1)=f(-2)+1 ......

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