$f:\mathbb R \to \mathbb R$ be a continuous such that $f(f(f(x)))=x,\forall x \in \mathbb R$ , is $f(x)=x , \forall x \in \mathbb R$?
16338
3rd iterate of a continuous function equals identity function
47381
If $\lim_{x\to\infty} [f(x+1)-f(x)] =l$ then $\lim_{ x\to\infty}f(x)/x =l$ ($f$ is continuous)
113687
$f$ is continuous function from $ [0,1]$ to itself and f(0)=0, f(1)=1 and $f(f(x))=x$ then show that $f(x)=x$ on$[0,1]$
72644
Continuous injective map $f:\mathbb{R}^3 \to \mathbb{R}$?
58597
A characterization of functions from $\mathbb R^n$ to $\mathbb R^m$ which are continuous
141223
$f(x^2) = 2f(x)$ and $f(x)$ continuous
44144
If $f:[a,b]\to \mathbb R$ is continuous then so is $\max_{t\in [a,x]}f(t)$?
33499
For which $a\in \mathbb{R}$ is $f(x,y) = \frac{xy^a}{x^2+y^2}$ with $f(0,0)=0$ continuous?
65946
A function $f: \mathbb R \to \mathbb R$ satisfies equation $f(x+y)=f(x)f(y)$ for all $x,y\in \mathbb R $
55605
If $f_n(x_n) \to f(x)$ whenever $x_n \to x$, show that $f$ is continuous
108115
If $f: [0,1]\rightarrow \mathbb{R}$ is continuous function positive
138864
If $f\colon \mathbb{R} \to \mathbb{R}$ is such that $f(x+y)=f(x)f(y)$ and $f'(0)$ exists, then $f$ is differentiable on $\mathbb R$
91852
A continuous, injective function $f: \mathbb{R} \to \mathbb{R}$ is either strictly increasing or strictly decreasing.
28111
Let $f:[1,10]\to \Bbb{Q}$ be a continuous function and $f(1)=10,$then $f(10)=?$
93461
Suppose that $f:\Bbb R\to \Bbb R$ is continuous and that $f(x)\to 0$ as $x\to \pm\infty.$Prove that $f$ is uniformly continuous.
23617
Determine whether $f(x)={\sin x \over x}$ is uniformly continuous in $\mathbb R$
90565
If $f:[0,1] \rightarrow \mathbb{R}$ is continuous function such that $f(0)=f(1)$ then there exists $ x\in [0,1]$ such that $f(x) = f(x+\frac{1}{n})$.