query: There exists a one-to-one function $g$ such that $f\circ g$ is constant
positive_passages.docid: 63836
positive_passages.text: Show there exists $g:(0,1)\to\mathbb{R}^2$ such that $h\circ g$ constant, $g$ continuously differentiable and $g$ injective
negative_passages.docid: 28399
negative_passages.text: Showing $f$ is constant
negative_passages.docid: 89473
negative_passages.text: Uniqueness of minimal polynomial: $f(x)$ divides $g(x)$
negative_passages.docid: 104044
negative_passages.text: Prove continuous functions $f$ and $g$ are equal
negative_passages.docid: 83163
negative_passages.text: If $X$ is a connected metric space, then a locally constant function $f: X \to $ M, $M $ a metric space, is constant
negative_passages.docid: 126065
negative_passages.text: Example $g\circ f=id_A$ but $f\circ g\neq id_B$
negative_passages.docid: 154001
negative_passages.text: $(g\circ f)^{-1}=f^{-1}\circ g^{-1}$
negative_passages.docid: 35787
negative_passages.text: An entire function with a bound on its integral is constant
negative_passages.docid: 11158
negative_passages.text: Proof that a continuous function with $f(x) = f(x^2)$ is constant.
negative_passages.docid: 61640
negative_passages.text: Prove c exists for f:[0,1] -> R
negative_passages.docid: 104757
negative_passages.text: If $f \circ g$ is surjective, then f is surjective
negative_passages.docid: 115636
negative_passages.text: Show that $f$ is either injective or a constant function.
negative_passages.docid: 91980
negative_passages.text: Prove that f is one-to-one on D
negative_passages.docid: 146572
negative_passages.text: Prove that between any two roots of $f$ there exists at least one root of $g$
negative_passages.docid: 13765
negative_passages.text: Is a rational-valued continuous function $f\colon[0,1]\to\mathbb{R}$ constant?
negative_passages.docid: 19146
negative_passages.text: Showing that $f$ has exactly one fixed point
negative_passages.docid: 143354
negative_passages.text: Prove that there exists $c\in\mathbb{R}$ such that $f'(c)=f(c)$