What is interesting about ffffffff...(x)?

Question

Does anyone know what is interesting about ffffff...(x), i.e. the function of itself many times over. Also written as f(f(f(f(f(f(f(x)))))))

For example if:

f(x) = 3x + 9
then what is special about repeating this, i.e.
ff(x) = 3(3x+9) +9
fff(x) = 3(3[3x+9]+9) + 9

and so on...?

Is there something interesting like a special pattern once they're all mutiplied out?

Best answer with clearest explanation scores 10 points!

Answer 1

1) If you define f(x)=1/x it will be:

f(x)=1/x
f(f(x))=x
f(f(f(x)))=1/x
...


2) If you define f(x)=x+a it will be:

f(x)=x+a
f(f(x))=x+2a
f(f(f(x)))=x+3a
...
f^n(x)=x+na

3) If you define f(x)=a-x it will be:

f(x)=a-x
f(f(x))=x
f(f(f(x)))=a-x
f(f(f(f(x))))=x
...
f^(2n-1)(x)=a-x
f^(2n)(x)=x

Be Succeed.

Answer 2

if the function is identity function or constant function, the result will be same.
Ex: f(x)=x
f(f(x))=x as you see.
In the same way
f(x)=c
c=constant number

f(f(x))=c

Because there is no x on the right to replace.

Answer 3

It reminds me of sex, the more you have sex the more you have pleasure.It is totally same so do stg practically, then will be able to get your answer soon...Good Luck

Answer 4

who t f cares ???