Does there exist a continuous function $f :\mathbb{R} \rightarrow \mathbb{R}$ such that $f \circ f(x) = -x$ for all $x$?
11453
Find a real function $f:\mathbb{R}\to\mathbb{R}$ such that $f(f(x)) = -x$?
109942
Find continuous functions such that $f(x+y)+f(x-y)=2[f(x)+f(y)]$
9320
Extension of continuous function on a closed subset of $\mathbb{R}$
15487
Continuous function from a connected set?
62817
Functions which are Continuous, but not Bicontinuous
141938
Find all continuous functions from positive reals to positive reals such that $f(x)^2=f(x^2)$
7036
Is there a bijective continuous function $f: \Bbb R \to \Bbb R$ whose inverse $f^{-1}$ is not continuous?
43189
Examples of continuous functions $f : \mathbb{R} \to \mathbb{R}$
145077
A continuous bijection $f:\mathbb{R}\to \mathbb{R}$ is an homeomorphism?
28011
Does there exists an entire function such that for each $|z|>C$ for some constant $C$, $|f(z)|=|z|+1$?
155618
Slightly changing the formal definition of continuity of $f: \mathbb{R} \to \mathbb{R}$?
77323
Existence of continuous angle function $\theta:S^1\to\mathbb{R}$
95970
Let $f:[0,1] \rightarrow \mathbb{R}$ be a continuous function. If $f(0)=f(1)$ then exists $x\in [0,1]$ s.t. $f(x) = f(x+\frac{1}{2})$
108115
If $f: [0,1]\rightarrow \mathbb{R}$ is continuous function positive
129551
Does $\lim_{h\rightarrow 0}\ [f(x+h)-f(x-h)]=0$ imply that $f$ is continuous?
126878
Monotonic function satisfying darboux property $\Rightarrow$ continuous
101319
Properties of a continuous map $f : \mathbb{R}^2\rightarrow \mathbb{R}$ with only finitely many zeroes