F^2(x)

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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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