Thread: 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.

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 then composed with itself 35 times is the same as composed with itself 5 times. So composed with itself 30 times must be the identity function. Therefore . So find the inverse function of and take its composition with itself. That will give you