query: Are they the same function? $y = x^2/x$ and $y = x$
positive_passages.docid: 17642
positive_passages.text: Why are removable discontinuities even discontinuities at all?
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: 105433
negative_passages.text: Graphing $y = \frac{x^2-4}{x-2}$
negative_passages.docid: 67214
negative_passages.text: Function $ y = x^n - nx$, where $x \geq 0$ and $n \geq 2$.
negative_passages.docid: 155757
negative_passages.text: Number theory: $x^y + 1 = y^x$
negative_passages.docid: 117392
negative_passages.text: Does $x^2 - y^2 = 12345678$ (x,y are integers) have any solutions?
negative_passages.docid: 50982
negative_passages.text: Is $\sqrt{x/a}+\sqrt{y/b}=1$ the equation of a parabola tangent to the coordinate axes?
negative_passages.docid: 24307
negative_passages.text: Is $x^x=y$ solvable for $x$?
negative_passages.docid: 20626
negative_passages.text: Prove that $x^y < y^x$
negative_passages.docid: 10444
negative_passages.text: If $\{x,\{x,y\}\} = \{z, \{z,t\}\}$, then must it be $x = z$ and $y = t$?
negative_passages.docid: 2038
negative_passages.text: What is the difference between linear regression on y with x and x with y?
negative_passages.docid: 142873
negative_passages.text: What does the function f: x ↦ y mean?
negative_passages.docid: 84189
negative_passages.text: Is $\mathbb{C}$ equal to $\mathbb{R}^2$?
negative_passages.docid: 65827
negative_passages.text: When $\min_{x \in X,y \in Y} f(x,y) = \min_{x \in X} \min_{y \in Y} f(x,y)$?
negative_passages.docid: 18761
negative_passages.text: Given that $x^y=y^x$, what could $x$ and $y$ be?
negative_passages.docid: 59658
negative_passages.text: Are $\mathrm{arccot}(x)$ and $\arctan(1/x)$ the same function?
negative_passages.docid: 22821
negative_passages.text: May $y=e^x$ be satisfied with both $x$ and $y$ $\in$ $\mathbb{Z}^+$?