Question

Dadas as funções reais f(x)= 1 -2x e
g(x) = x +k, o valor de k, de modo que f(g(x)) = g(f(x)), é:

Answer 1

f (x) = 1 - 2x
g(x) = x + k


k => f(g(x)) = g (f(x))
1- 2x = x + k
1-2 (x+k) = (1-2x ) + k
1 - 2x -2k = 1-2x + k
-3 k - 2x + 2x -1 +1=0
-3 k = 0
k=0