# Can this fuctional equation be solved? [duplicate]

$f: \mathbb{R}^{+} \rightarrow \mathbb{R}^{+}$

$f(x^2)=xf(x)$

$f(x+1)=f(x)+1$

Can this functional equation be solved ?

• Yes, it can be solved by you. – Watson Jun 12 '18 at 14:18
• Or at the very least, attempted by you. – Rhys Hughes Jun 12 '18 at 14:21
• For $f$ continuous this has been solved on MSE here. – Dietrich Burde Jun 12 '18 at 14:34

Perhaps obvious but what about $$f(x)=x?$$