f(f(x))= (9x^2 +6x+2)f(x) f(x)=?


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Question Number 158668 by cortano last updated on 07/Nov/21

$f (f (x)) = (9 x^{2} + 6 x + 2) f (x)$ $f (x) = ?$
	Answered by ajfour last updated on 07/Nov/21

	$A s s u m i n g f (x) i s a p o l y n o m e . .$ $n^{2} = n + 2$ $\Rightarrow n = 2, n = - 1$ $c a s e (1)$ $s o f i r s t l e t f (x) = {p x}^{2} + q x + r$ $p {({p x}^{2} + q x + r)}^{2} + q ({p x}^{2} + q x + r)$ $+ r = (9 x^{2} + 6 x + 2) ({p x}^{2} + q x + r)$ $c o m p a r i n g c o e f f i c i e n t s$ $w e f i n d p, q, r .$ $c a s e (2)$ $f (x) = \frac{p}{x} + q$ $\frac{p}{(\frac{p}{x} + q)} + q = (9 x^{2} + 6 x + 2) (\frac{p}{x} + q)$
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