The No. of Continuous function satisfying the condition $xf(y)+yf(x)=(x+y)f(x)f(y)$
50833
Find all $f:\mathbb R\to\mathbb R$ such that $\forall x,y\in\mathbb R$ the given equality holds: $xf(y)+yf(x)=(x+y)f(x)f(y)$.
129599
Functional Equation: Find all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ such that $(x+y)(f(x)-f(y))=(x-y)f(x+y)$
111556
Solving functional equation $f(x+y)+f(x-y)=2f(x)\cos y$?
11158
Proof that a continuous function with $f(x) = f(x^2)$ is constant.
103934
Functional Equation (no. of solutions): $f(x+y) + f(x-y) = 2f(x) + 2f(y)$
37966
If $f$ is continuous and $f(x+y) = f(x)+f(y)$, then $f(x) = cx$ for all $x \in \mathbb{R}$
148227
Rewriting of functional equation $f(xy)=f(x)+f(y)$
122329
Determine all functions $f(x)$ such that $f(f(x+y))=f(x)+f(y)$
26754
Find all continuous functions satisfying $\int_0^xf=(f(x))^2+C$ for some constant $C \neq 0$.
37976
Find all functions $f$ such that $(x+y)f(x)+f(y^2)=(x+y)f(y)+f(x^2)$
97104
Proof that continuous function on $ [0, 2]$ has $f(x) = f(x-1)$ for some $ x$
41226
Find $f:f(xf(x)+f(y))=f(x)^2+y$
62723
If $f\colon \mathbb{R} \to \mathbb{R}$ is such that $f (x + y) = f (x) f (y)$ and continuous at $0$, then continuous everywhere
77943
If $f$ is continuous, then there exists $x+\frac{1}{n}\in[0,1]$ and $f\left(x+\frac{1}{n}\right)=f(x)$
11828
continuous functions on $\mathbb R$ such that $g(x+y)=g(x)g(y)$
69707
If $f(x + y) \leq yf(x) + f(f(x))$ for all real numbers $x$ and $y$, then prove that $f(x) = 0$ for all $x ≤ 0$.
409
functions satisfying $f(x - y) = f(x) f(y) - f(a - x) f(a + y)$ and $f(0)=1$