# Find all such functions $f:R\to R$

It's my last question. Just give me advise how to start.

Q: Find all such functions $$f:\mathbb R\to \mathbb R,$$ for all real x, y, the equality $$f(yf(x))=x^2y^4$$

• are the function continuous ? derivable ? – idm Nov 22 '14 at 9:27
• Show that f(1) is not 0. – Paul Nov 22 '14 at 9:36
• Function are contimuos. – Vlad9pa Nov 22 '14 at 9:36

$f(yf(1))=y^4,$ so $f(1)\ne0$, so $f(y)=\left(\frac{y}{f(1)}\right)^4$. Now putting $y=1$ in last equation we get $f(1)=1$ and $f(y)=y^4$. Now it is easy too see that $f(y)=y^4$ cannot satisfy the equation $f(yf(x))=x^2y^4$