Continuous functions such that $f(x)+f(x^2)=x$
41201
How prove there is no continuous functions $f:[0,1]\to \mathbb R$, such that $f(x)+f(x^2)=x$.
69734
how to find all functions such that $f\left( x^{2} - y^{2} \right) = ( x - y )( f(x) + f(y) )$
68165
Find a function $f: \mathbb{R} \to \mathbb{R}$ that is continuous at precisely one point?
156778
Finding functions satisfying $f(f(x))+f(x)+x=0$
2321
Can there be two distinct, continuous functions that are equal at all rationals?
77943
If $f$ is continuous, then there exists $x+\frac{1}{n}\in[0,1]$ and $f\left(x+\frac{1}{n}\right)=f(x)$
2142
Finding a set of continuous functions with a certain property 2
71738
Continuously differentiable function iff $|f(x + h) - f(x + t) - l(h - t)| \leq \epsilon |h-t|$
141223
$f(x^2) = 2f(x)$ and $f(x)$ continuous
25010
Argue that there exists a continuous function $g: \mathbb{R} \rightarrow \mathbb{R}$ which satisfies $g(x) = \frac{1-e^{-2x^2}}{x^2}$ for $x \neq 0$
44670
Find all functions $f: \mathbb Z \to \mathbb Z$ such that $f(x+y)=f(x)+f(y)$
136594
Proving the existence of a sequence of polynomials convergent to a continuous function $f$.
29647
Do there exist functions satisfying $f(x+y)=f(x)+f(y)$ that aren't linear?
14975
Functions satisfying $f:\mathbb{N}\rightarrow\ \mathbb{N}$ and $f(f(n))+f(n+1)=n+2$
13927
Values of $a$ s.t. for all continuous $f$ with $f(0)=f(1)$ there exists $x$ s.t. $f(x+a) = f(x)$
85092
Proving $ f(x) = x^2 $ is not uniformly continuous on the real line
128911
Continuous extension of a real function