Question

Sejam f(x)=x-3 e g(x)=x^2-2x+4. Para qual valor de x tem f(g(x))=g(f(x))?

Answer 1

f(g (x))= x-3
f(x^2 -2x + 4)= x -3
f(x^2 -2x +4) = x^2 -2x + 4 -3
f(g (x)) = x^2 -2x +1

g (f (x))= x^2 -2x + 4
g (x-3)= (x -3)^2 + 4
g (x-3)= (x -3) . (x-3) + 4
g (x-3)= x^2 -3x -3x + 9 +4
g (x-3)= x^2 -6x + 13