perplexus.info :: Just Math : Positively Real

Positively Real (Posted on 2012-09-09)

R⁺denotes the set of positive real numbers.

Determine all possible functions f:R⁺→ R⁺ such that:

f(f(x)) = 12x - f(x) for all x > 0.

No Solution Yet Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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Possible Answer

| Comment 1 of 4

f(x) = -4x

f(x) = 3x

I think these may be the only solutions. I have a way of showing why and will present when I have more time.

Posted by Chris, PhD on 2012-09-09 18:44:18

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