Question

se f(x)=3x+4 e g(x)=2x + 2k, calcule o valor de k para que se tenha (fog)(x)=(gof)(x)

Answer 1

f(g(x))=g(f(x))
f(x)=3x+4
g(x)=2x+2k
f(g(x))=3.(2x+2k)+4
f(g(x))=6x+6k+4
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g(f(x))=2.(3x+4)+2k
g(f(x))=6x+8+2k
6x+6k+4=6x+8+2k
6x-6x+6k-2k=8-4
4k=4
k=4/4
k=1 #