Question

Determinar função inversa de $y=\frac{3x-2}{4x+3} | x \neq - \frac{3}{4}$

Answer 1

Despejemos a x

$\displaystyle y=\frac{3x-2}{4x+3}\iff y(4x+3)=3x-2\\ \\ y=\frac{3x-2}{4x+3}\iff 4xy+3y=3x-2\\ \\ y=\frac{3x-2}{4x+3}\iff 4xy-3x=-3y-2\\ \\ y=\frac{3x-2}{4x+3}\iff x(4y-3)=-3y-2\\ \\ y=\frac{3x-2}{4x+3}\iff x=-\frac{3y+2}{4y-3}\\ \\ \text{Ent\~ao, a inversa \'e }g(y)=-\frac{3y+2}{4y-3} \text{ ou igualmente }\boxed{g(x)=-\frac{3x+2}{4x-3}}$