Find all functions $f:\mathbb R \to \mathbb R$ that satisfy $f(x) + 3 f\left( \frac {x-1}{x} \right) = 7x$ for all nonzero $x$.
140978
Real domain and range function to find all functions with nonzero x.
41201
How prove there is no continuous functions $f:[0,1]\to \mathbb R$, such that $f(x)+f(x^2)=x$.
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 $
52858
Find $f$ if $ f(x)+f\left(\frac{1}{1-x}\right)=x $
68165
Find a function $f: \mathbb{R} \to \mathbb{R}$ that is continuous at precisely one point?
41226
Find $f:f(xf(x)+f(y))=f(x)^2+y$
1071
Determine all functions $f:\mathbb{N}\rightarrow\mathbb{N}$ such that $xf(y)+yf(x)=(x+y)f(x^2+y^2)$ for all $x,y\in\mathbb{N}$ (contest question)
95970
Let $f:[0,1] \rightarrow \mathbb{R}$ be a continuous function. If $f(0)=f(1)$ then exists $x\in [0,1]$ s.t. $f(x) = f(x+\frac{1}{2})$
142769
Let $f(x) =7x^{32}+5x^{22}+3x^{12}+x^2$. Then find its remainder in the following cases.
32432
Strategies to find the set of functions $f:\mathbb R\to\mathbb R$ satisfing the functional equation: $f(x^3)+f(y^3)=(x+y)(f(x^2)+f(y^2)-f(xy))$
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 $x \neq 0$
26169
Function $f: \mathbb{R} \to \mathbb{R}$ that takes each value in $\mathbb{R}$ three times
28286
About finding the function such that $f(xy)=f(x)f(y)-f(x+y)+1$
156778
Finding functions satisfying $f(f(x))+f(x)+x=0$
24810
Functions satisfying $(b-a)f'(\tfrac{a+b}{2}) = f(b)- f(a)$
118873
Prove that $f(x)=0$ for all $x\in\mathbb{R}$.
11453
Find a real function $f:\mathbb{R}\to\mathbb{R}$ such that $f(f(x)) = -x$?