query: Show that $f(x + 1/n) = f(x)$ for some $x$, given $f(0) = f(1)$
positive_passages.docid: 8913
positive_passages.text: Show that there is $\xi$ s.t. $f(\xi)=f\left(\xi+\frac{1}{n}\right)$
negative_passages.docid: 143491
negative_passages.text: Show that $f$ is differentiable on $(−1, 1)$.
negative_passages.docid: 132093
negative_passages.text: Solve $f(f(x))=f(x)$
negative_passages.docid: 25775
negative_passages.text: How to prove $(1+1/x)^x$ is increasing when $x>0$?
negative_passages.docid: 130829
negative_passages.text: The function $f (n) = (1 + 1 / n) ^ {n+1}$ is decreasing
negative_passages.docid: 51659
negative_passages.text: If $f(0)=0$ then prove that $|f(z)+f(-z)| \leq 2|z|^2$
negative_passages.docid: 21891
negative_passages.text: If $f(xy)=f(x)f(y)$ then show that $f(x) = x^t$ for some t
negative_passages.docid: 13202
negative_passages.text: Prove that there exists at least one $x_0\in\mathbb{R}$, such that $f(x_0)+f''(x_0)=0$
negative_passages.docid: 45885
negative_passages.text: If there exist sequence such that $g(x_n)=f(x_{n+1})$, then we have $g(x_0)=f(x_0)$ for some $x_0$
negative_passages.docid: 156778
negative_passages.text: Finding functions satisfying $f(f(x))+f(x)+x=0$
negative_passages.docid: 83738
negative_passages.text: Prove $(k,n+k)=1$ iff $(k,n)=1$
negative_passages.docid: 88147
negative_passages.text: Show that $g_n(x)=nf(x+1/n)-nf(x)$ converges uniformly to $f'$
negative_passages.docid: 95575
negative_passages.text: If $f(s) = (1+s)^{(1+s)^{(1+s)/s}/s}$, show that $\lim_{s \to \infty} f(s)/s = 1$.
negative_passages.docid: 35556
negative_passages.text: $f(z)=\frac{z}{1+|z|} $ Is 1-1?
negative_passages.docid: 13248
negative_passages.text: How to obtain $f(x)$, if it is known that $f(f(x))=x^2+x$?
negative_passages.docid: 149739
negative_passages.text: Prove: $f(t)\leq t+1$
negative_passages.docid: 43246
negative_passages.text: Showing that if $a<b$, then $a^{1/n} < b^{1/n}$