query: Example for $c(fg)\neq c(f)c(g)$
positive_passages.docid: 145191
positive_passages.text: Content of a polynomial
negative_passages.docid: 83036
negative_passages.text: f(g(x)) has a degree divisible by n
negative_passages.docid: 139111
negative_passages.text: Prove that $a<c<b$, $\frac{f(b)-f(a)-(b-a)f'(a)}{g(b)-g(a)-(b-a)g'(a)}=\frac{f"(c)}{g"(c)}$
negative_passages.docid: 35547
negative_passages.text: Does $\{f_ng_n\}\to fg$ uniformly?
negative_passages.docid: 122330
negative_passages.text: Prove that there exists some $c\in(-3,3)$ such that$ \ \ g(c) \cdot g''(c)<0$.
negative_passages.docid: 110103
negative_passages.text: Prove that there are $0<c_1 < c_2<1$ s.t. $\frac{1}{g'(c_1)}+\frac{1}{g'(c_2)}=2$ . The same for $g'(c_1)g'(c_2)=1$.
negative_passages.docid: 149399
negative_passages.text: Given continuous $f$ and $g$, there exists $c \in (a,b)$ such that $\int_{a}^{c} f(x) \ \mathrm dx = \int_{c}^{b} g(x) \ \mathrm dx$
negative_passages.docid: 135701
negative_passages.text: An example of a group such that $G \cong G \times G$
negative_passages.docid: 63701
negative_passages.text: An example of a regular function over an open set
negative_passages.docid: 1821
negative_passages.text: Proving $f(C) \setminus f(D) \subseteq f(C \setminus D)$ and disproving equality
negative_passages.docid: 11828
negative_passages.text: continuous functions on $\mathbb R$ such that $g(x+y)=g(x)g(y)$
negative_passages.docid: 32127
negative_passages.text: Example where $f\circ g$ is bijective, but neither $f$ nor $g$ is bijective
negative_passages.docid: 98474
negative_passages.text: Show the existence of a certain subgroup of F2
negative_passages.docid: 8742
negative_passages.text: Examples and further results about the order of the product of two elements in a group
negative_passages.docid: 56413
negative_passages.text: $f(g(x))=g(f(x))$ implies $f(c)=g(c)$ for some $c$
negative_passages.docid: 113411
negative_passages.text: If $E$ is generated by $E_1$ and $E_2$, then $[E:F]\leq [E_1:F][E_2:F]$?
negative_passages.docid: 146152
negative_passages.text: Characterising functions $f$ that can be written as $f = g \circ g$?