query: Can a continuous real function take each value exactly 3 times?
positive_passages.docid: 26169
positive_passages.text: Function $f: \mathbb{R} \to \mathbb{R}$ that takes each value in $\mathbb{R}$ three times
negative_passages.docid: 108997
negative_passages.text: Continuous functions that attain local extrema at every point
negative_passages.docid: 97773
negative_passages.text: If $f$ is continuous with $f(x) = f(2x),f(1) = 3$, then what is $ \int_{-1}^{1}f(f(x))\,dx$?
negative_passages.docid: 11828
negative_passages.text: continuous functions on $\mathbb R$ such that $g(x+y)=g(x)g(y)$
negative_passages.docid: 130149
negative_passages.text: Computablility of a real number
negative_passages.docid: 66560
negative_passages.text: Is a differentiable function always continuous?
negative_passages.docid: 80656
negative_passages.text: Is it possible to iterate a function transfinite times?
negative_passages.docid: 4538
negative_passages.text: Is the mapping $ d : X\times X \mapsto \mathbb {R} $ continuous?
negative_passages.docid: 83338
negative_passages.text: Show that there's no continuous function that takes each of its values $f(x)$ exactly twice.
negative_passages.docid: 26955
negative_passages.text: Continuous at exactly two points and differentiable at exactly one of them
negative_passages.docid: 62817
negative_passages.text: Functions which are Continuous, but not Bicontinuous
negative_passages.docid: 139763
negative_passages.text: A function takes every function value twice - proof it is not continuous
negative_passages.docid: 2321
negative_passages.text: Can there be two distinct, continuous functions that are equal at all rationals?
negative_passages.docid: 47992
negative_passages.text: Is there a function $f\colon\mathbb{R}\to\mathbb{R}$ such that every non-empty open interval is mapped onto $\mathbb{R}$?
negative_passages.docid: 727
negative_passages.text: Prove that any continuous integer-valued function of a real variable is constant.
negative_passages.docid: 72115
negative_passages.text: Why isn't there a continuously differentiable surjection from $I \to I \times I$?
negative_passages.docid: 109942
negative_passages.text: Find continuous functions such that $f(x+y)+f(x-y)=2[f(x)+f(y)]$