f-f-n-2n-f-n-

Question Number 32743 by naka3546 last updated on 01/Apr/18

f (f (n)) = 2 n

f (n) = ?

Commented by abdo imad last updated on 03/Apr/18

i f f i s a p o l y n o m i a l f o f (x) = 2 x \Rightarrow f^{,} (f (x)) f^{^{'}} (x) = 2 \Rightarrow y^{,} (y) = \frac{2}{y^{^{'}}}

d e g f = p \Rightarrow {d e g f}^{^{'}} = p - 1 \Rightarrow 2 (p - 1) = 0 \Rightarrow p = 1 \Rightarrow f (x) = λ x

f (f (x)) = 2 x \Rightarrow f (λ x) = 2 x \Rightarrow λ (λ x) = 2 x \forall x \Rightarrow λ^{2} = 2 \Rightarrow

λ = \bar{+} \sqrt{2} a n d f (x) = \bar{+} \sqrt{2} x

Answered by Joel578 last updated on 02/Apr/18

f (n) = a n

f (f (n)) = f (a n) = a (a n) = a^{2} n = 2 n

a = \pm \sqrt{2}

f (n) = \pm n \sqrt{2}

Answered by MJS last updated on 01/Apr/18

f (n) = \pm n \sqrt{2}

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