query: Non-linear function such that $f(ax)=af(x)$ for every $a \in \mathbb R, x \in \mathbb R^n$
positive_passages.docid: 113572
positive_passages.text: Are all multiplicative functions additive?
negative_passages.docid: 23186
negative_passages.text: $f: \mathbb{R^2} \to \mathbb{R}$ a $C^\infty$ function such that $f(x,0)=f(0,y)=0$ then exists $g$ such that $f(x,y)=xy\, g(x,y)$
negative_passages.docid: 82597
negative_passages.text: How to find $ f(x)$ if $f(1-f(x))=x$ for all $x$ $\in \mathbb{R}$
negative_passages.docid: 17421
negative_passages.text: Linear Algebra: Find a matrix A such that T(x) is Ax for each x
negative_passages.docid: 125788
negative_passages.text: A function with a property $f(x+y)=f(x)f(y)$
negative_passages.docid: 69876
negative_passages.text: For every $n \in \mathbb{N}$, find a function $f$ which is differentiable $n$ times at $0$, but not $n+1$ times.
negative_passages.docid: 409
negative_passages.text: functions satisfying $f(x - y) = f(x) f(y) - f(a - x) f(a + y)$ and $f(0)=1$
negative_passages.docid: 98255
negative_passages.text: Find $f(x)$ such that $f(f(x)) = x^2 - 2$
negative_passages.docid: 60306
negative_passages.text: Natural class of functions whose $\mathcal O$-sets are linearly ordered
negative_passages.docid: 48652
negative_passages.text: Solve the functional equation $2f(x)=f(ax)$ for some $a$.
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: 20568
negative_passages.text: Does the following have a solution for f(x,y)?
negative_passages.docid: 24553
negative_passages.text: $f$ has the form $f(x) =ax^2+bx+c$.
negative_passages.docid: 31898
negative_passages.text: Sufficient conditions for $x, Ax, A^2x, ...$ being linearly indepedent
negative_passages.docid: 146152
negative_passages.text: Characterising functions $f$ that can be written as $f = g \circ g$?
negative_passages.docid: 17406
negative_passages.text: Determine all the extrema of a function subject to a non-linear constraint.
negative_passages.docid: 140978
negative_passages.text: Real domain and range function to find all functions with nonzero x.