Question

considerando-se as funçoes f(x)= 3x+2 e g(x)= -2x+1, pode-se afirmar que (fog-¹)(x )é definida por:

Answer 1

$f(x)=3x+2\\ g(x)=-2x+1\\ \\ \\ Inversa:\\ y=-2x+1\\ x=-2y+1\\ 2y=-x+1\\ g^{ -1 }=\frac { -x+1 }{ 2 } \\ \\ f(g^{ -1 }(x))\\ \\ f(g^{ -1 }(x))=3(\frac { -x+1 }{ 2 } )+2\\ \\ f(g^{ -1 }(x))=\frac { -3x+1 }{ 2 } +2\\ \\ f(g^{ -1 }(x))=-3x+1+4\\ \\ f(g^{ -1 }(x))=-3x+5$