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a fost răspuns

Se considera functia f:R->R, f(x)=x+2.Sa se rezolve ecuatia f(f(x))=f^2(x)

Răspuns :

Albatran
f(x+2) =(x+2)²
x+2+2=x²+4x+4
x+4=x²+4x+4
x²+3x=0
x1=0
x2=-3
verificare f(0)=2
 f(2)=2+2=4
f(0)²=2²=4

f(-3)=-1
f(-1)=-1+2=1
(f(-3))²=(-1)²=1