f-f-x-9x-2-6x-2-f-x-f-x-

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)

Facebook Tweet Pin