Question

3. Dadas as funções f(x) = 2x+a e g(x) = 3x-1, determine o valor de a para que se tenha f(g(x))= g(f(x)).​

Answer 1

$f(x) = 2x + a\\g(x) = 3x - 1\\\\f(g(x)) = 2.(3x - 1) + a = 6x - 2 + a\\g(f(x)) = 3.(2x + a) - 1 = 6x + 3a - 1\\\\f(g(x)) = g(f(x)) \\6x - 2 + a = 6x + 3a - 1\\-2 + a = 3a - 1\\3a - a = -2 + 1\\2a = -1\\a = -\frac{1}{2}$