Solve $f(f(x))=f(x)$
59063
$f(f(x))=f(x)$ question
65418
Solve these functional equations: $\int_0^1\!{f(x)^2\, \mathrm{dx}}= \int_0^1\!{f(x)^3\, \mathrm{dx}}= \int_0^1\!{f(x)^4\, \mathrm{dx}}$
26562
Inverse of $f(x)=\sin(x)+x$
147325
Proving that if $f(x)=x$ has no real solution then $f(f(x))=x$ has no real solution either
73519
Determine all functions satisfying $f(x + f(x + y)) + f(xy) = x + f(x + y) +yf(x)$
126931
Find $f(x)$ such that $f(x)+f\left(\frac{1}{x}\right)=f(x)\cdot f\left(\frac{1}{x}\right)$
111556
Solving functional equation $f(x+y)+f(x-y)=2f(x)\cos y$?
144090
How to solve the functional equation $f\left(x^2+f(y)\right)=y+f(x)^2$
103934
Functional Equation (no. of solutions): $f(x+y) + f(x-y) = 2f(x) + 2f(y)$
111789
Solving functional differential equation $f'(x)=2f(2x)-f(x)$
26677
thoughts about $f(f(x))=e^x$
129599
Functional Equation: Find all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ such that $(x+y)(f(x)-f(y))=(x-y)f(x+y)$
62966
Find all functions $f(x)$ such that $f\left(x^2+f(y)\right)$=$y+(f(x))^2$
104278
Finding function $f(x)$ which satisfy given functional equation
133333
Find $f(x)$ for $f(f(x))=\sin x$
129052
Find all functions satisfying $\frac{1}{f(a)}+ \frac{1}{f(b)} = \frac{1}{f(c)} $ whenever $\frac{1}{a}+ \frac{1}{b} = \frac{1}{c} $
21891
If $f(xy)=f(x)f(y)$ then show that $f(x) = x^t$ for some t