Question

3- As funções f(x) = 3–4x e g(x) = 3x+m são tais que f(g(x)) = g(f(x)), qualquer que seja x real. O valor de m é:
a) 9/4
b) 5/4
c) –6/5
d) 9/5
e) –2/3

Answer 1

Resposta:

Explicação passo-a-passo:

$f(x)=3-4x\\\\g(x)=3x+m\\\\f(g(x))=g(f(x))\\\\3-4.(3x+m)=3.(3-4x)+m\\\\3-12x-4m=9-12x+m\\\\3-4m=9+m\\\\invertendo\\\\9+m=3-4m\\\\m+4m=3-9\\\\5m=-6\\\\m=-\dfrac{6}{5}$

Item c)