New posts in Functional Equations

If $f(x)=f(2x)$, then $f$ is differentiable

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

Solve functional equation $ h(y)+h^{-1}(y)=2y+y^2 $

Hard functional equation: $ f \big ( x y + f ( x ) \big) = f \big( f ( x ) f ( y ) \big) + x $

Determine all $P(x) \in \mathbb R[x]$ such that $P(x^2) + x\big(mP(x) + nP(-x)\big) = \big(P(x)\big)^2 + (m - n)x^2$, $\forall x \in \mathbb R$.

Defining sine and cosine from functional equations $(S(x))^2+(C(x))^2=1$, $C(x+y)=C(x)C(y)-S(x)S(y)$, etc

Functional equation problem: $ f \left( y ^ 2 - f ( x ) \right) = y f ( x ) ^ 2 + f \left( x ^ 2 y + y \right) $

How to show that $f(x)\equiv x$?

I am learning functional equation and encountered $f(f(x)-x)=x$.

Find all additive real valued functions such that $f(x^{2019})=f(x)^{2019}$