Answer
$y = \frac{1}{4}x - 2$
Work Step by Step
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:
$y = \frac{1}{4}x - 2$
