Question

Sejam f e g funções nodulares reais definidas por f(x)= |x+2| e g(x)= 2 |x-2|. Resolva a equação f(x)= g(x). Urgente i

Answer 1

f(x)= |x+2| e g(x)= 2.|x-2|

Igualando as funções acima:

$|x+2| = 2.|x-2|\Rightarrow\\\\{\frac{|x+2|}{|x-2|} = 2} \Rightarrow \\\\|{\tfrac{x+2}{x-2}}| = 2 \Rightarrow\\\\{\tfrac{x+2}{x-2}} = 2~~ou~~{\tfrac{x+2}{x-2}}=-2\\\\x+2 = 2.(x-2) ~~ou~~x+2=-2.(x-2)\\\\x+2 = 2.x - 4~~ou~~x+2=-2x+4\\\\\boxed{x = 6~~ou~~x=\frac{2}{3}}$