Solve the equation f(f(x))=f^2(x), where f(x)=x+2, f being a real function.

We notice that f(f(x)) is the composition law: f composed
with f.

f(f(x))= f(x)+2=
x+2+2=x+4

f(f(x))= x+4

f^2(x)=
(x+2)^2=
x^2+2x+4

x^2+4x+4=x+4

x^2+4x+4-x-4=0

x^2+3x=0

x(x+3)=0

If
a product between 2 factors is zero, that means that one of them is
zero.

x=0

x+1=0

x=-3