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-

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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