Question

Sejam f e g funções de R em R, sendo R o conjunto dos numeros reais, dadas por f(x)=3x-4 e f(g(x))=2x+1 nestas condições g(2) é igual a

Answer 1

$\displaystyle \sf f(x) = 3x-4 \\\\ \underline{\text{Fa{\c c}amos x = g(x) }} : \\\\ f(g(x)) = 3g(x) - 4 \\\\ \underline{\text{por{\'em} f(g(x)) = 2x+1, da{\'i}}} : \\\\ 3g(x) - 4 = 2x+1 \\\\ 3g(x) = 2x+1+4 \\\\ 3g(x) = 2x+5 \\\\ g(x) = \frac{2x+5}{3} \\\\\\ x= 2 \therefore \ g(2) = \frac{2\cdot 2+5 }{3} \to g(2) =\frac{4+5}{3} \to g(2) = \frac{9}{3} \\\\ Portanto : \\\\ \huge\boxed{\sf g(2) = 3 } \checkmark$