query: Function satisfying $f(2x^2-1)=(x^3+x)f(x)$
positive_passages.docid: 147184
positive_passages.text: $f:[-1,1]\to \mathbb{R}$ is a continuous function such that $f(2x^2-1)=(x^3+x)f(x).$ Find $\lim_{x\to 0}\frac {f(\cos x)}{\sin x}$
negative_passages.docid: 144773
negative_passages.text: function $f(x)=x^{-(1/3)}$ , please check whether my solution is correct?
negative_passages.docid: 132093
negative_passages.text: Solve $f(f(x))=f(x)$
negative_passages.docid: 105497
negative_passages.text: A function satisfying a series equation
negative_passages.docid: 3885
negative_passages.text: Maximum and minimum of of $f(x)=|x-1|+|x-2|+|x-3|$
negative_passages.docid: 39090
negative_passages.text: Finding functions such that $f(g(x)) = f(x)g(x)$
negative_passages.docid: 104949
negative_passages.text: How would I prove that this function is affine if $f(x+h)-f(x)=hf'(x)$?
negative_passages.docid: 78632
negative_passages.text: Summation equation for $2^{x-1}$
negative_passages.docid: 53024
negative_passages.text: $f(x)f(1/x)=f(x)+f(1/x)$
negative_passages.docid: 97104
negative_passages.text: Proof that continuous function on $ [0, 2]$ has $f(x) = f(x-1)$ for some $ x$
negative_passages.docid: 24862
negative_passages.text: Solving (quadratic) equations of iterated functions, such as $f(f(x))=f(x)+x$
negative_passages.docid: 37976
negative_passages.text: Find all functions $f$ such that $(x+y)f(x)+f(y^2)=(x+y)f(y)+f(x^2)$
negative_passages.docid: 144859
negative_passages.text: Finding parameters for $f(x) = x^2 + 2(m − a)x + 3am −2 = 0$ that satisfy a condition.
negative_passages.docid: 59063
negative_passages.text: $f(f(x))=f(x)$ question
negative_passages.docid: 28286
negative_passages.text: About finding the function such that $f(xy)=f(x)f(y)-f(x+y)+1$
negative_passages.docid: 125788
negative_passages.text: A function with a property $f(x+y)=f(x)f(y)$
negative_passages.docid: 409
negative_passages.text: functions satisfying $f(x - y) = f(x) f(y) - f(a - x) f(a + y)$ and $f(0)=1$