g(((x−1)/(x+1)))=((7x+3)/(x+1)) and f(x^2 −2x+3)=3x^2 −6x+7 find (f+g)(x)=?


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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

	${You}^{'} re welcome!$
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