query: How to solve the question related to continuity.
positive_passages.docid: 154034
positive_passages.text: Suppose that $f(x)$ is continuous on $(0, \infty)$ such that for all $x > 0$,$f(x^2) = f(x)$. Prove that $f$ is a constant function.
negative_passages.docid: 57642
negative_passages.text: Uniform Continuity implies Continuity
negative_passages.docid: 67249
negative_passages.text: Can you determine a formula for this problem?
negative_passages.docid: 142519
negative_passages.text: Uniqueness and Existence problem
negative_passages.docid: 99858
negative_passages.text: Cumulative distribution function and right continuity
negative_passages.docid: 143951
negative_passages.text: Can we determine uniform continuity from graphs?
negative_passages.docid: 46834
negative_passages.text: show that a distance function is continuous
negative_passages.docid: 149354
negative_passages.text: Proof of continuity $f(x+y) = f(x) + f(y)$
negative_passages.docid: 104268
negative_passages.text: Confusion on how to solve this question about sequences.
negative_passages.docid: 140153
negative_passages.text: Conjectures Involving floor(x)/piecewise continuity with regards to Integration and Differential Equations
negative_passages.docid: 110327
negative_passages.text: How to do this question that talks about dependency of x
negative_passages.docid: 34940
negative_passages.text: Continuity of $f(x) = x^n$
negative_passages.docid: 98666
negative_passages.text: Continuity defined for rational and irrational numbers
negative_passages.docid: 130023
negative_passages.text: Prove that the sum of two continuous functions is continuous
negative_passages.docid: 57180
negative_passages.text: Techniques to prove a function is uniformly continuous
negative_passages.docid: 153798
negative_passages.text: Problem involving maximum and minimum of a continuous function
negative_passages.docid: 141223
negative_passages.text: $f(x^2) = 2f(x)$ and $f(x)$ continuous