Find $f(2a-x)$ from the given equation $f(x-y)=f(x)\cdot f(y)-f(a-x)\cdot f(a+y)$ and $f(0)=1$
409
functions satisfying $f(x - y) = f(x) f(y) - f(a - x) f(a + y)$ and $f(0)=1$
18903
Finding solutions to equation of the form $1+x+x^{2} + \cdots + x^{m} = y^{n}$
157744
Cauchy's functional equation with composite function: $gf(x+y)=gf(x)+gf(y)$
13248
How to obtain $f(x)$, if it is known that $f(f(x))=x^2+x$?
4178
Solve $f(x)f(2x^2) = f(2x^3+x)$
132093
Solve $f(f(x))=f(x)$
66772
$f(f(x)f(y))+f(x+y)=f(xy)$
101289
Studying the equation $\ln(x)- 1+ x^2=0$
59063
$f(f(x))=f(x)$ question
66404
Prove that:$\int_{a}^{b} f(x) dx = b \cdot f(b) - a \cdot f(a) - \int_{f(a)}^{f(b)} f^{-1}(x) dx$
148227
Rewriting of functional equation $f(xy)=f(x)+f(y)$
98255
Find $f(x)$ such that $f(f(x)) = x^2 - 2$
131692
How to show that $f_{0}f_{1}+f_{1}f_{2}+...+f_{2n-1}f_{2n} = f^{2}_{2n}$
129902
If $f(x)=x+\int_{0}^{1}[xy^2+x^2y]f(y)dy$ where $x$ and$y$ are independent variable.Find $f(x).$
142682
Find $f(x)$ where $ f(x)+f\left(\frac{1-x}x\right)=x$
49794
Solve $f(x^2+y+f(y))=2y+f(x)^2$ over $\mathbb{R}$
126931
Find $f(x)$ such that $f(x)+f\left(\frac{1}{x}\right)=f(x)\cdot f\left(\frac{1}{x}\right)$