Answer
$f^{-1}(x) = -\frac{7x-28}{5}$
Work Step by Step
$f(x) = -\frac{5}{7}x +4$
Let $f(x) = y$:
$y = -\frac{5}{7}x +4$
Switch the variables $x$ and $y$ to find the inverse and solve for $y$:
$x = -\frac{5y}{7} +4$
$x - 4 = -\frac{5y}{7}$
$x - 4 = \frac{-5y}{7}$
$7x - 28 = -5y$
$y = -\frac{7x-28}{5}$
$f^{-1}(x) = -\frac{7x-28}{5}$
