Question

Sabendo que f(x)=2x-5 e g (x)=3x+m, determinar m de modo que f(g(x))=g(f(x))

Answer 1

f(x) = 2x - 5

g(x) = 3x + m

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

f(3x + m) = g(2x - 5)

2.(3x + m) - 5 = 3.(2x - 5) + m

6x + 2m - 5 = 6x - 15 + m

2m - m = 6x - 6x - 15 + 5

m = -10

Prova real:

f(x) = 2x - 5

g(x) = 3x - 10

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

f(3x - 10) = g(2x - 5)

2.(3x - 10) - 5= 3.(2x - 5) - 10

6x - 20 - 5= 6x - 15 - 10

6x - 25 = 6x - 25