Homework Help: Stuck on this function

I'm going through the review section of the Stewart Calculus text and I'm stuck on this problem.

Given
[itex]
f_0(x) = x^2
[/itex]
and
[itex]
f_0(f_n(x)) = f_{n+1}(x) , n = 0,1,2...
[/itex]
how do you solve for
[itex]
f_n(x)
[/itex]

 

The only place I can think to start is making [itex] (f_n(x))^2 = f_{n+1}(x) [/itex], but that's as far as I got

 

From that I get [itex] f_n(x) = x^{2^{n+1}} [/itex] but that doesn't work for [itex] f_0(x) = x^2 [/itex]. That's the same answer the book has, so maybe I wrote the requirements down wrong. I'll have to check when I get home if this had to work for 0.

 

Yes it does. Never mind.

Thanks Viet Dao!