Possible Duplicate:
$f(x+1)=f(x)+1$ and $f(x^2)=f(x)^2$
Let $f:\mathbb{R}\to\mathbb{R}$ be a function such that for all reals $x$
$f(x^2)=f(x)^2$ and $f(x+1)=f(x)+1$
Can we show that $f(x)=x$ for all reals $x$? Do we need additional assumptions in order to prove that $f(x)=x$ for all reals $x$ (like continuity, differentiability or monotony)? If so, try to give an example of a function $f$ different from $f(x)=x$ that satisfies all the stuff above.
