g-x-1-x-1-7x-3-x-1-and-f-x-2-2x-3-3x-2-6x-7-find-f-g-x-

Question Number 154200 by amin96 last updated on 15/Sep/21

g (\frac{x - 1}{x + 1}) = \frac{7 x + 3}{x + 1} a n d f (x^{2} - 2 x + 3) = 3 x^{2} - 6 x + 7

f i n d (f + g) (x) = ?

Answered by Rasheed.Sindhi last updated on 15/Sep/21

g (\frac{x - 1}{x + 1}) = \frac{7 x + 3}{x + 1} a n d f (x^{2} - 2 x + 3) = 3 x^{2} - 6 x + 7

f i n d (f + g) (x) = ?

▸ \frac{x - 1}{x + 1} = y \Rightarrow x - 1 = x y + y \Rightarrow x = \frac{y + 1}{1 - y}

g (y) = \frac{7 (\frac{y + 1}{1 - y}) + 3}{(\frac{y + 1}{1 - y}) + 1} = \frac{7 y + 7 + 3 - 3 y}{y + 1 + 1 - y} = \frac{4 y + 10}{2}

g (y) = 2 y + 5 \Rightarrow g (x) = 2 x + 5

▸ f (x^{2} - 2 x + 3) = 3 x^{2} - 6 x + 7 = 3 x^{2} - 6 x + 9 - 2

f (x^{2} - 2 x + 3) = 3 (x^{2} - 2 x + 3) - 2

L e t x^{2} - 2 x + 3 = y

f (y) = 3 y - 2 \Rightarrow f (x) = 3 x - 2

(f + g) (x) = (2 x + 5) + (3 x - 2)

▸ (f + g) (x) = 5 x + 3

Commented by amin96 last updated on 15/Sep/21

n i c e w o r k . t h a n k s s i r

Commented by Rasheed.Sindhi last updated on 15/Sep/21

{You}^{'} re welcome!