query: Solutions of $f(x)\cdot f(y)=f(x\cdot y)$
positive_passages.docid: 21891
positive_passages.text: If $f(xy)=f(x)f(y)$ then show that $f(x) = x^t$ for some t
negative_passages.docid: 134043
negative_passages.text: Prove that for $ f(x+2\cdot\pi)=f(x), x \in \mathbb{R} $, there exists $ x_0 $ so $ f(x_0+\pi)=f(x_0) $
negative_passages.docid: 138931
negative_passages.text: Show that $||x+y||\cdot||x-y||\le||x||^2+||y||^2$
negative_passages.docid: 134880
negative_passages.text: Is there a difference between $y(x)$ and $f(x)$
negative_passages.docid: 103019
negative_passages.text: Find all functoins $f: \mathbb R \rightarrow \mathbb R$ such that $\forall x,y \in \mathbb R f(xy+f(x))=xf(y)+f(x)$
negative_passages.docid: 133682
negative_passages.text: Prove that if $f(t)$ satisfies $f(t)=f'(t)$, then $f(t+s)=f(t)f(s)$ for all $t,s\in R$ without using the fact that $f(t)=c\cdot e^t$.
negative_passages.docid: 66404
negative_passages.text: Prove that:$\int_{a}^{b} f(x) dx = b \cdot f(b) - a \cdot f(a) - \int_{f(a)}^{f(b)} f^{-1}(x) dx$
negative_passages.docid: 4178
negative_passages.text: Solve $f(x)f(2x^2) = f(2x^3+x)$
negative_passages.docid: 76458
negative_passages.text: Solve the following functional equation $f(xf(y))+f(yf(x))=2xy$
negative_passages.docid: 29647
negative_passages.text: Do there exist functions satisfying $f(x+y)=f(x)+f(y)$ that aren't linear?
negative_passages.docid: 39090
negative_passages.text: Finding functions such that $f(g(x)) = f(x)g(x)$
negative_passages.docid: 32599
negative_passages.text: Solution to the functional equation $f(x^y)=f(x)^{f(y)}$
negative_passages.docid: 81921
negative_passages.text: If $f(x + y) = f(x) + f(y)$ showing that $f(cx) = cf(x)$ holds for rational $c$
negative_passages.docid: 62254
negative_passages.text: Show $F_{n+1} \cdot F_{n-1} = F_n^2 + (-1)^n$ for all $n \in \mathbb{N}$
negative_passages.docid: 147325
negative_passages.text: Proving that if $f(x)=x$ has no real solution then $f(f(x))=x$ has no real solution either
negative_passages.docid: 41226
negative_passages.text: Find $f:f(xf(x)+f(y))=f(x)^2+y$
negative_passages.docid: 103251
negative_passages.text: Solution(s) to $f(x + y) = f(x) + f(y)$ (and miscellaneous questions...)