# Thread: form of functions f (x) and g (x)

1. ## form of functions f (x) and g (x)

can you help me to find the set of functions f (x) and g (x) that satisfy the two following relations respectively

f (x + c) = c + f (x)and
g (x + c) = c + g ^ 2 (x)
with c is a non-zero constant

2. ## Re: form of functions f (x) and g (x)

Let $\displaystyle h(x)= f(x)-x$ and show that $\displaystyle h(x+c)=h(x)$ for all $\displaystyle x$

meaning $\displaystyle h$ is periodic of period $\displaystyle c$

3. ## Re: form of functions f (x) and g (x)

Originally Posted by popovyoussef
can you help me to find the set of functions f (x) and g (x) that satisfy the two following relations respectively

f (x + c) = c + f (x)and
g (x + c) = c + g ^ 2 (x)
with c is a non-zero constant
Does $g^2(x)$ mean $g(g(x))$ or does it mean $(g(x))^2$?