Determine all continuous real function which satisfies the following
11453
Find a real function $f:\mathbb{R}\to\mathbb{R}$ such that $f(f(x)) = -x$?
26754
Find all continuous functions satisfying $\int_0^xf=(f(x))^2+C$ for some constant $C \neq 0$.
14495
I need to find all functions $f:\mathbb R \rightarrow \mathbb R$ which are continuous and satisfy $f(x+y)=f(x)+f(y)$
131992
A problem on continuous functions
53812
Metric is continuous function
61500
If f is continous and exist real numbers show that $f(x)=0$
23617
Determine whether $f(x)={\sin x \over x}$ is uniformly continuous in $\mathbb R$
88586
show that every continuous real-valued function defined on $S_{\mathbb{\Omega}}$ is eventually constant
54797
Find the continuous function defined over $[0,1]$ such that $\int_0^1f(x){\rm d}x=1, \int_0^1 xf(x){\rm d}x=a$ and $\int_0^1x^2f(x){\rm d}x=a^2 .$
97104
Proof that continuous function on $ [0, 2]$ has $f(x) = f(x-1)$ for some $ x$
136011
Must $f$ be continuous?
100740
proof of that a continuous function has a fixed point
143174
property of continuous function
14578
Proving that an additive function $f$ is continuous if it is continuous at a single point
151410
Inequality of continuous functions
34836
Composition of Absolutely Continuous Functions
33330
Continuous Functions from $\mathbb{R}$ to $\mathbb{Q}$