SOLUTION: if f0(x)=1/1-x and Fn+1= f0 o fn for n = 0,1,2,....find f100(3)

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: if f0(x)=1/1-x and Fn+1= f0 o fn for n = 0,1,2,....find f100(3)      Log On


   

Question 382693: if f0(x)=1/1-x and Fn+1= f0 o fn for n = 0,1,2,....find f100(3)
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
We have f1(3) = -1/2, f2(3) = 2/3, f3(3) = 3, f4(3) = -1/2, etc.
Since the recursive sequence only depends on the previous term, we conclude that
f(3n) (3) = 3
f(3n+1) (3) = -1/2
f(3n+2) (3) = 2/3
Since 100 is 1 modulo 3, f100(3) = f1(3) = -1/2.