query: Give an example for $f(A)\setminus f(F) \neq f(A\setminus F)$.
positive_passages.docid: 1821
positive_passages.text: Proving $f(C) \setminus f(D) \subseteq f(C \setminus D)$ and disproving equality
negative_passages.docid: 120235
negative_passages.text: Clarification of the notation $f: \mathbb{R} \setminus\{3\} \to\mathbb{R}\setminus\{2\}$
negative_passages.docid: 68746
negative_passages.text: What is $f(f^{-1}(A))$?
negative_passages.docid: 126065
negative_passages.text: Example $g\circ f=id_A$ but $f\circ g\neq id_B$
negative_passages.docid: 151958
negative_passages.text: How to show $f'(0)$ exist and is equal to $1$?
negative_passages.docid: 106748
negative_passages.text: Number of functions $f : A \to A$ such that $f(f(x))=f(x)$
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: 59279
negative_passages.text: Example of function that is differentiable, but the second derivative is not defined
negative_passages.docid: 156778
negative_passages.text: Finding functions satisfying $f(f(x))+f(x)+x=0$
negative_passages.docid: 13927
negative_passages.text: Values of $a$ s.t. for all continuous $f$ with $f(0)=f(1)$ there exists $x$ s.t. $f(x+a) = f(x)$
negative_passages.docid: 80421
negative_passages.text: Show that $a - b \mid f(a) - f(b)$
negative_passages.docid: 94680
negative_passages.text: Holomorphic function $f$ such that $f'(z_0) \neq 0$
negative_passages.docid: 129716
negative_passages.text: Let $f$ be continuous on $ [a,b]$, differentiable on $ (a,b) $ and $ f(x) \neq 0 \forall x \in (a,b) $ Prove $ \exists c \in (a,b) $ such that
negative_passages.docid: 111756
negative_passages.text: How do I prove that then $f(x) = 1$ for some $x ∈ [0, 1]$?
negative_passages.docid: 80199
negative_passages.text: Do we have always $f(A \cap B) = f(A) \cap f(B)$?
negative_passages.docid: 13270
negative_passages.text: Prove $\exists \xi \in (a,b):f'(\xi)<1+f^2(\xi)$
negative_passages.docid: 135199
negative_passages.text: Looking for a function $f$ that is $n$-differentiable, but $f^{(n)}$ is not continuous