Question

as funções f()=3-4x e g(x)=3x+m tais que f(g(x)e=g(f(x). qualquer que seja x real o valor de m é?

Answer 1

f(x) = 3 - 4x

g(x) = 3x + m

f(g(x)) = 3 - 4 (3x+m) = 3 - 12x -4m
f(g(x)) = 3 - 12x -4m


g(f(x)) = 3(3-4x) + m = 9 -12x +m
g(f(x)) = 9 -12x +m

f(g(x)) = g(f(x))

3 - 12x- 4m = 9 -12x +m
-4m -m = -3+12x+9-12x
-5m = 6
m = 6/-5
m = -6/5