# How do you find the inverse of f(x)=(3x-2)/(x+7)?

${f}^{- 1} x = \frac{7 x + 2}{3 - x}$
$y = f \left(x\right) = \frac{3 x - 2}{x + 7} = \frac{3 x + 21 - 23}{x + 7} = 3 - \frac{23}{x + 7}$
$y = 3 - \frac{23}{x + 7} \implies \left(y - 3\right) = - \frac{23}{x + 7} \implies x + 7 = \frac{23}{3 - y} \implies x = - 7 + \frac{23}{3 - y}$
${f}^{- 1} y = - 7 + \frac{23}{3 - y} = \frac{7 y + 2}{3 - y}$
$\implies {f}^{- 1} x = \frac{7 x + 2}{3 - x}$