Question

Qual é a função inversa de f (x) = x+3 / x-3 ?

Answer 1

$y=f(x)=\frac{x+3}{x-3} \\\\ y=\frac{x+3}{x-3} \\\\ x=\frac{y+3}{y-3} \\\\ (y-3) . x = y + 3 \\\\ y-3=\frac{y+3}{x} \\\\ y=\frac{y+3}{x} + 3 \\\\ \frac{xy=y+3+3x}{x} \\\\ xy = y +3 +3x \\\\ xy -y = 3x +3 \\\\ y(x-1)=3x+3 \\\\ y=\frac{3x+3}{x-1} \\\\ y=f^{-1} (x)=3\frac{x+1}{x-1} \\\\ f^{-1} (x)=3\frac{(x+1)}{x-1}$