If is an even function defined on the interval (−5,5) then a value of x satisfying the equation f(x)=f(((x+1)/(x+2))) is a)((−1+(√5))/2) b)((−3+(√5))/2) c)((−1−(√5))/2) d)((−3−(√5))/2


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Question Number 44351 by Necxx last updated on 27/Sep/18

$I f i s a n e v e n f u n c t i o n d e f i n e d o n$ $t h e i n t e r v a l (- 5, 5) t h e n a v a l u e$ $o f x s a t i s f y i n g t h e e q u a t i o n$ $f (x) = f (\frac{x + 1}{x + 2}) i s$ $a) \frac{- 1 + \sqrt{5}}{2} b) \frac{- 3 + \sqrt{5}}{2} c) \frac{- 1 - \sqrt{5}}{2}$ $d) \frac{- 3 - \sqrt{5}}{2_{}}$
Commented by Necxx last updated on 27/Sep/18

$p l e a s e h e l p$
	Answered by MrW3 last updated on 27/Sep/18

	$f (x) = f (- x)$ $f (x) = f (\frac{x + 1}{x + 2})$ $c a s e 1 : \frac{x + 1}{x + 2} = x$ $x + 1 = x^{2} + 2 x$ $x^{2} + x - 1 = 0$ $\Rightarrow x = \frac{- 1 \pm \sqrt{5}}{2}$ $c a s e 2 : \frac{x + 1}{x + 2} = - x$ $x + 1 = - x^{2} - 2 x$ $x^{2} + 3 x + 1 = 0$ $\Rightarrow x = \frac{- 3 \pm \sqrt{5}}{2}$ $a) b) c) d) a r e a l l c o r r e c t .$
	Commented by Necxx last updated on 27/Sep/18

	$T h a n k y o u s i r . I a p p r e c i a t e .$
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