Question

determine a função inversa em cada caso a) f(x)= 2x+1/3x-1​

Answer 1

Para determinar a inversa, vamos seguir 2 passos:

--> Trocar "x" por "y"  (Lembrar: f(x) = y);

--> Isolar "y".

$y~=~\dfrac{2x+1}{3x-1}\\\\\\Trocando~"x"~por~"y":\\\\\\x~=~\dfrac{2y+1}{3y-1}\\\\\\Isolando~"y":\\\\\\x~.~(3y-1)~=~2y+1\\\\\\3xy-x~=~2y+1\\\\\\3xy-2y~=~1+x\\\\\\y.(3x-2)~=~1+x\\\\\\\boxed{f^{-1}(x)~=~y~=~\dfrac{1+x}{3x-2}}$