Question

considerando as funções f(x)= 4x+m e g(x)=2x-6, determine m para que (fog)=(gof).

Answer 1

(fog)(x) = f(g(x)) = 4(2x - 6) + m = 8x - 24 + m

(gof)(x) = g(f(x)) = 2(4x + m) - 6 = 8x + 2m - 6 

(fog)(x) = (gof)(x) ⇒ 8x - 24 + m = 8x + 2m - 6 ⇒ m - 2m = - 6 + 24

- m = 18 ⇒ m = - 18