Question

Função composta, eu achei alternativa C, 1/5. Quanto vcs acham?

Answer 1

Resposta:

Letra B

Explicação passo-a-passo:

Descobrindo $g^{-1}(1)$

$y=\frac{2x+3}{5x-1} \\\\y.(5x-1)=2x+3\\\\5xy-y=2x+3\\\\5xy-2x=3+y\\\\x(5y-2)=3+y\\\\x=\frac{3+y}{5y-2}\\\\x=\frac{3+1}{5.1-2}\\\\x=\frac{4}{3}$

Substituindo na segunda equação

$f(g^{-1}(1))=x^2-2x+1\\\\f(g^{-1}(1))=(\frac{4}{3} )^2-2\ {\cdot}\ (\frac{4}{3} )x+1\\\\f(g^{-1}(1))=\frac{16}{9} -\frac{8}{3} +1\\\\f(g^{-1}(1))=\frac{16-24+9}{9}\\\\f(g^{-1}(1))=\frac{1}{9}$