The-function-pogof-x-x-4-2x-3-2x-2-is-divisible-by-the-half-of-the-function-of-p-Find-g-x-

Question Number 55621 by Tawa1 last updated on 28/Feb/19

The function pogof (x) = x^{4} + {2 x}^{3} + {2 x}^{2} is divisible by the half of the

function of p . Find g (x) .

Answered by kaivan.ahmadi last updated on 28/Feb/19

2 p (g o f (x)) = 2 x^{2} (x^{2} + 2 x + 2)

d i v i d e p (x) \Rightarrow p (x) = 2 x^{2}

\Rightarrow g (f (x)) = x^{2} + 2 x + 2 = {(x + 1)}^{2} + 1

t h e n g (x) = x^{2} + 1 a n d f (x) = x + 1 i s

o n e o f t h e a n s w e r s .

g e n e r a l l y g (x) = {(x - k)}^{2} + 1

a n d f (x) = x + k + 1 i s a n s w e r

t h i s q u e s t i o n h a s n o u n i q u e a n s w e r

t = f (x) \Rightarrow f^{- 1} (t) = x

g (t) = {(f^{- 1} (t) + 1)}^{2} + 1