# How many polynomials of degree >=1 satisfy $f({x^2}) = {[f(x)]^2} = f(f(x)$

a) more than 2
b) 2
c) 0
d) 1
asked Nov 1, 2013 in TCS

Let f(x) = ${x^2}$
$f({x^2}) = {[{x^2}]^2} = {x^4}$
${\left( {f(x)} \right)^2} = {[{x^2}]^2} = {x^4}$
$f(f(x)) = f({x^2}) = {[{x^2}]^2} = {x^4}$