query: Can I say $|f(x)g(x)|=||fg||$
positive_passages.docid: 76140
positive_passages.text: The supremum norm is submultiplicative
negative_passages.docid: 45222
negative_passages.text: When $f(x) = g(y)$ for almost every $(x,y)$, must $f$ and $g$ be constant almost everywhere?
negative_passages.docid: 132971
negative_passages.text: Prove that $|a| < b \iff -b<a<b$
negative_passages.docid: 94571
negative_passages.text: How can we prove that $N_G(H)=H$ implies $N_{f(G)}(f(H))=f(H)$
negative_passages.docid: 26207
negative_passages.text: If $f$ is a quadratic and $f(x)>0\;\forall x$, and $g= f + f' + f''$, prove $g(x)>0\; \forall x$
negative_passages.docid: 77074
negative_passages.text: If $ f(f(f(x)))=x$, does$ f(x)=x$ necessarily follow?
negative_passages.docid: 120960
negative_passages.text: $f,g$ such that $\int fg = \int f \int g$
negative_passages.docid: 146152
negative_passages.text: Characterising functions $f$ that can be written as $f = g \circ g$?
negative_passages.docid: 57938
negative_passages.text: When do two functions become equal?
negative_passages.docid: 7858
negative_passages.text: Proving that $f(x)$ is irreducible over $F(b)$ if and only if $g(x)$ is irreducible over $F(a)$
negative_passages.docid: 3387
negative_passages.text: Derivative of $f(x)=|x|$
negative_passages.docid: 152438
negative_passages.text: Is the composition of two injective functions injective?
negative_passages.docid: 17310
negative_passages.text: Can $f(x)=|x|^3$ be differentiated
negative_passages.docid: 149122
negative_passages.text: If two functions are defined by the same formula, but have different codomains, are they equal?
negative_passages.docid: 113329
negative_passages.text: Let $S=\{1,2,3,4,\dotsc,N\}$ and $X=\{ f: S \rightarrow S \mid x < y \Rightarrow f(x)\leqslant f(y)\}$. Then $|X|$ is equal to what?
negative_passages.docid: 56492
negative_passages.text: Does the order of $f(x)$ divide the order of $x$ if $f$ is a group homomorphism?
negative_passages.docid: 144018
negative_passages.text: Integration by parts for f(x).g(x)