## Algebra 1: Common Core (15th Edition)

$y = \frac{1}{4}x - 2$
First, rewrite the equation with $f(x)$ replaced with $y$: $y = 4x - 2$ To find the inverse of a function, we replace $y$ with $x$ and $x$ with $y$: $x = 4y - 2$ Now we solve for $y$. First, subtract the $y$ term from each side of the equation to have $y$ terms on the left side of the equation: $x - 4y = -2$ Subtract $x$ from each side of the equation to isolate the $y$ term: $-4y = -x - 2$ Divide each side by $-4$ to solve for $y$: $y = \frac{-1}{-4}x - 2$ Divide both the numerator and denominator of the fraction by $-1$ to simplify: $y = \frac{1}{4}x - 2$