query: There exist two functions f, g satistfying: $\int f(x)·g(x)dx = \int f(x)dx ·\int g(x) dx$?
positive_passages.docid: 120960
positive_passages.text: $f,g$ such that $\int fg = \int f \int g$
negative_passages.docid: 142494
negative_passages.text: Functions $f(x)/g(x), g(x)/h(x),h(x)/f(x)$ are constant
negative_passages.docid: 72694
negative_passages.text: Proving that $f(x) = g(x)$ for some $x \in [a,b]$ if $f,g$ continuous, $f(a)  g(b)$
negative_passages.docid: 158327
negative_passages.text: #define f(g,g2) g##g2
negative_passages.docid: 134070
negative_passages.text: $g$ a restriction of a homeomorphic function $f$, $g$ also homeomorphic?
negative_passages.docid: 144146
negative_passages.text: find a $\int_{x}^{g(x)} f(t)\,dt = 1$
negative_passages.docid: 146152
negative_passages.text: Characterising functions $f$ that can be written as $f = g \circ g$?
negative_passages.docid: 133851
negative_passages.text: How to arrive at $\int_{0}^{1} f^3(x) \, dx < (\int_{0}^{1} f(x) \, dx)^2$?
negative_passages.docid: 11453
negative_passages.text: Find a real function $f:\mathbb{R}\to\mathbb{R}$ such that $f(f(x)) = -x$?
negative_passages.docid: 57938
negative_passages.text: When do two functions become equal?
negative_passages.docid: 126065
negative_passages.text: Example $g\circ f=id_A$ but $f\circ g\neq id_B$
negative_passages.docid: 30694
negative_passages.text: Show that there exist $[a,b]\subset [0,1]$, such that $\int_{a}^{b}f(x)dx$ = $\int_{a}^{b}g(x)dx$ = $\frac{1}{2}$
negative_passages.docid: 98823
negative_passages.text: Let $g:\mathbb{R}\to\mathbb{R}$ be a measurable function such that $g(x+y) =g(x)+g(y).$ Then $g(x) = g(1)x$ .
negative_passages.docid: 112566
negative_passages.text: Let $f,g$ be two distinct functions from $[0,1]$ to $(0, +\infty)$ such that $\int_{0}^{1} g = \int_{0}^{1} f $.
negative_passages.docid: 40047
negative_passages.text: Is $\int_a^b f(x) dx = \int_{f(a)}^{f(b)} f^{-1}(x) dx$?
negative_passages.docid: 74810
negative_passages.text: A function $f$ such that $f' = 0$ when $x < 0$ and $f' = 1$ when $x \geq 0$?
negative_passages.docid: 72254
negative_passages.text: Is that true that not every function $f(x,y)$ can be writen as $h(x) g(y)$?