If-f-x-f-x-1-f-x-1-where-f-10-6-and-f-20-2f-21-then-f-16-

Question Number 154668 by EDWIN88 last updated on 20/Sep/21

I f f (x) = f (x - 1) + f (x + 1) w h e r e

f (10) = 6 a n d f (20) = 2 f (21)

t h e n f (16) = \dots ?

Commented by mathdanisur last updated on 20/Sep/21

f (16) = - f (21)

f (21) = - 6 \Rightarrow f (16) = 6

Commented by Rasheed.Sindhi last updated on 20/Sep/21

M o r e d e t a i l s p l e a s e!

Answered by Rasheed.Sindhi last updated on 20/Sep/21

f (x) = f (x - 1) + f (x + 1)

f (x) - f (x - 1) = f (x + 1)

A p p l y i n g d e f i n i t i o n o n l e f t s i d e :

f (x) - f (x - 1) = f (x) + f (x + 2)

f (x - 1) = - f (x + 2)

x - 1 \to x

f (x) = - f (x + 3)

▸ f (10) = - f (13) = 6 \Rightarrow f (13) = - 6

▸ f (13) = - f (13 + 3) = - 6

f (16) = 6

Commented by mathdanisur last updated on 20/Sep/21

Very nice Ser

Commented by Rasheed.Sindhi last updated on 20/Sep/21

T h a n k s s e r!