Question 1151834
<pre>We know that substituting a power of x into a power of x gives a power of
x, so we try to see if f(x)=x<sup>n</sup> gives a solution:

If so then try

f(x) = x<sup>n</sup>

then 

f(f(x)) = f(x<sup>n</sup>) = (x<sup>n</sup>)<sup>n</sup> = x<sup>n²</sup> = x<sup>2</sup>

The one and only way that can be true for all x is if the exponents of x are
equal

So n²=2

or

{{{n="" +- sqrt(2)}}}

So one solution is

{{{matrix(2,1,"","f(x)"=x^sqrt(2))}}}

Another solution is

{{{matrix(2,1,"","f(x)"=x^(-sqrt(2)))}}}

Can there be other solutions???

Edwin</pre>