Question

f(x) = 1-f(x-1) For positive integer x, if f(2)=12, then compute f(2006).

Answer 1

Oh god lol

Answer 2

oops that x=2 one sec

Answer 3

\[f(2)=1-f(2-1)=1-f(1)=12=> f(1)=-11\]

Answer 4

\[f(3)=1-f(2)=1-12=-11\]
\[f(4)=1-f(3)=1-(-11)=12\]
\[f(5)=1-f(4)=1-12=-11\]

Answer 5

Thank you! But what about f(2006)? I'm confused on how to incorporate that..

Answer 6

i think there may be a pattern

Answer 7

I see..

Answer 8

\[f(6)=1-f(5)=1-(-11)=12\]
\[f(7)=1-f(6)=1-12=-11\]

Answer 9

see its either -11 or 12

Answer 10

all odds are -11 evens are 12

Answer 11

right

Answer 12

Wow, thanks so much you guys! First time using this site and I love it already. (: