# Find simple expression for f28

• Mar 16th 2011, 06:22 AM
chris86
Find simple expression for f28
For the functions
f1(x)=(2x-1)/(x+1)
f(n+1)(x)=f1(fn(x)) for n>=1
it can be shown that f35=f5.Find the simple expression for f28.
• Mar 16th 2011, 10:26 AM
Opalg
Quote:

Originally Posted by chris86
For the functions
f1(x)=(2x-1)/(x+1)
f(n+1)(x)=f1(fn(x)) for n>=1
it can be shown that f35=f5.Find the simple expression for f28.

If $f_{35} = f_5$ then $f_1$ composed with itself 35 times is the same as $f_1$ composed with itself 5 times. So $f_1$ composed with itself 30 times must be the identity function. Therefore $f_{28} = f_{-2}$. So find the inverse function of $f_1$ and take its composition with itself. That will give you $f_{-2}.$