If • f(2x + 1) + g(3 − x) = x • f(((3x + 5)/( x + 1))) + 2g(((2x + 1)/(x + 1))) = (x/(x + 1)) for every x ∈ R, x ≠ −1 Find f(x) !!


Question and Answers Forum

All Questions Topic List
Relation and Functions Questions
Previous in All Question Next in All Question
Previous in Relation and Functions Next in Relation and Functions
Question Number 10987 by Joel576 last updated on 05/Mar/17

$If$ $∙ f (2 x + 1) + g (3 - x) = x$ $∙ f (\frac{3 x + 5}{x + 1}) + 2 g (\frac{2 x + 1}{x + 1}) = \frac{x}{x + 1}$ $for every x \in R, x \neq - 1$ $Find f (x)!!$
	Answered by ajfour last updated on 05/Mar/17

	$\frac{(3 x - 7)}{2} i s i t ?!$
	Commented by ajfour last updated on 05/Mar/17

	$s t a r t i n g w i t h t h e s e c o n d,$ $f (3 + \frac{2}{x + 1}) + 2 g (2 - \frac{1}{x + 1}) = \frac{(x + 1) - 1}{x + 1}$ $i f \frac{1}{x + 1} \to y (w e s a y)$ $f (3 + 2 y) + 2 g (2 - y) = \frac{1 / y - 1}{1 / y} = 1 - y$ $i f n o w y \to y - 1, t h e n$ $f (2 y + 1) + 2 g (3 - y) = 2 - y;$ $o r f (2 x + 1) + 2 g (3 - x) = 2 - x$ $s u b t r a c t i n g t h i s e q n f r o m$ $2 f (2 x + 1) + 2 g (3 - x) = 2 x (i n q u e s t i o n)$ $w e g e t : f (2 x + 1) = 3 x - 2$ $i f x \to x - \frac{1}{2}, f (x) = 3 (x - \frac{1}{2}) - 2$ $f (x) = (3 x - 7) / 2 .$
	Commented by Joel576 last updated on 08/Mar/17

	$t h a n k y o u v e r y m u c h$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum