What functions satisfy f(f(x))=f(x) for any real x?
132093
Solve $f(f(x))=f(x)$
140978
Real domain and range function to find all functions with nonzero x.
1440
Are the any non-trivial functions where $f(x)=f'(x)$ not of the form $Ae^x$
59063
$f(f(x))=f(x)$ question
68165
Find a function $f: \mathbb{R} \to \mathbb{R}$ that is continuous at precisely one point?
55175
Is the function $f(x) = x^2 - 2x$ one-to-one?
37976
Find all functions $f$ such that $(x+y)f(x)+f(y^2)=(x+y)f(y)+f(x^2)$
125788
A function with a property $f(x+y)=f(x)f(y)$
122329
Determine all functions $f(x)$ such that $f(f(x+y))=f(x)+f(y)$
132488
Find all entire functions $f(z)$ such that $|f(z)|=1$ for $|z|=1$
62966
Find all functions $f(x)$ such that $f\left(x^2+f(y)\right)$=$y+(f(x))^2$
28011
Does there exists an entire function such that for each $|z|>C$ for some constant $C$, $|f(z)|=|z|+1$?
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 $
50552
find functions that $f(m+k)=f(mk-n)$
129599
Functional Equation: Find all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ such that $(x+y)(f(x)-f(y))=(x-y)f(x+y)$
39090
Finding functions such that $f(g(x)) = f(x)g(x)$
11453
Find a real function $f:\mathbb{R}\to\mathbb{R}$ such that $f(f(x)) = -x$?