Answer
$g^{-1}(x) = 4x+3 $
Work Step by Step
$g(x) = \frac{1}{4}x - \frac{3}{4}$
Let $g(x) = y$:
$y = \frac{1}{4}x - \frac{3}{4}$.
Switch the variables $x$ and $y$ to find the inverse and solve for $y$:
$x = \frac{1}{4}y - \frac{3}{4}$
$x = \frac{y}{4}- \frac{3}{4}$
$x + \frac{3}{4}= \frac{y}{4}$
$4x + 3 = y$
$y = 4x + 3$
$g^{-1}(x) = 4x+3 $.
