# Functional equations

Hello,

could you explain me what's the right way to solve these equations. i've never solved it before.

$$f(x+y)+f(x-y)=2f(x)f(y)\,\;\;\forall x,y\in\mathbb{R}$$
$$f(x)+\left(x+\frac{1}{2}\right)f(1-x)=1\,\;\;\forall x\in\mathbb{R}$$

thank you............

## Answers and Replies

Hello,

could you explain me what's the right way to solve these equations. i've never solved it before.

$$f(x+y)+f(x-y)=2f(x)f(y)\,\;\;\forall x,y\in\mathbb{R}$$
$$f(x)+\left(x+\frac{1}{2}\right)f(1-x)=1\,\;\;\forall x\in\mathbb{R}$$

thank you............
Since the equation is true for all values, use clever values of x and y to get a system of equations.

HallsofIvy