For every set of $x_i$ there exists a point $x \in \mathbb{R}$ such that: $f(x) = \sqrt[n]{f(x_1) \cdot f(x_2) \cdot f(x_3) \cdot ... \cdot f(x_n)}$
12240
Problem with a continuous function
39321
If $f:\mathbb R \to \mathbb R$ satisfies $f'(x) <L$ for some $L<1$, then $f$ has a unique fixed point
143067
Show given any $x\in\mathbb{R}$ show there exists a unique $n\in\mathbb{Z}$ such that $n-1\leq x <n$.
96618
Any finite set of points in in the projective plane can be defined by two polynomials
67234
The function $G: x \mapsto 2^{x^2}$ maps $\mathbb{R}$ onto $\{ x \in \mathbb{R} : x \geq 1 \}$
82405
For f continuous on $[0,1]$, show that there exist points $\alpha_k$ such that $\sum \limits_{k=1}^n \frac{1}{f'(\alpha_k)} = n $
6582
Prove the existence of the square root of $2$.
35133
Every increasing function from a certain set to itself has at least one fixed point
21457
Prove $\sqrt{2\sqrt{3\sqrt{\cdots\sqrt{n}}}}<3$ by induction.
33734
Every closed subset $E\subseteq \mathbb{R}^n$ is the zero point set of a smooth function
111756
How do I prove that then $f(x) = 1$ for some $x ∈ [0, 1]$?
49240
$\forall x,y \in \mathbb{R}:\vert\cos x- \cos y\vert\leq\vert x-y\vert$
14277
Proving $f(x)=x\cdot |x|$ is a bijection
54729
Prove that $f$ has a fixed point .
84510
If $f(\mathbb{C})\subset \mathbb{C}-[0,1]$ then $f$ is constant
42292
Show that $a_n<\sqrt{2}$ for every $n\in\mathbb{N}$.
82597
How to find $ f(x)$ if $f(1-f(x))=x$ for all $x$ $\in \mathbb{R}$