Question

PUC-RJ 2012 Sejam f(x) = 2x + 1 e g(x) = 3x + 1. Então f(g(3)) - g(f(3)) é igual a:

Answer 1

$\boxed{\mathrm{f(x)=2x+1}}\ \ \mathrm{e}\ \ \boxed{\mathrm{g(x)=3x+1}}\\\\ \mathbf{Calculando\ f(g(3)):}\\\\ \mathrm{f(g(x))=2.g(x)+1=2(3x+1)+1=}\\ \mathrm{=6x+2+1=6x+3\ \to\ f(g(x))=6x+3}\\\\ \mathrm{f(g(3))=6.3+3=18+3=\boxed{21}}\\\\ \mathbf{Calculando\ g(f(3)):}\\\\ \mathrm{g(f(x))=3.f(x)+1=3(2x+1)+1=}\\ \mathrm{=6x+3+1=6x+4\ \to\ g(f(x))=6x+4}\\\\ \mathrm{g(f(3))=6.3+4=18+4=\boxed{22}}\\\\ \mathbf{Logo:}\\\\ \mathrm{f(g(3))-g(f(3))=21-22=\boxed{\boxed{-1}}}$