# Stuck on this function

1. Sep 27, 2005

### Jeff Ford

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

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

Last edited: Sep 27, 2005
2. Sep 27, 2005

### Jeff Ford

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

3. Sep 27, 2005

### VietDao29

Now, f1(x) = f0(f0(x)) = f0(x2) = x4
f2(x) = f0(f1(x)) = f0(x4) = x8
f3(x) = f0(f2(x)) = ...
f4(x) = f0(f3(x)) = ...
So what's fn(x)?
Can you go from here?
Viet Dao,

4. Sep 27, 2005

### Jeff Ford

From that I get $f_n(x) = x^{2^{n+1}}$ but that doesn't work for $f_0(x) = x^2$. 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.

5. Sep 27, 2005

### Jeff Ford

Yes it does. Never mind.

Thanks Viet Dao!