Answer
$y = 2x - 2$
Work Step by Step
First, rewrite the equation with $f(x)$ replaced with $y$:
$y = \frac{1}{2}x + 1$
To find the inverse of a function, we replace $y$ with $x$ and $x$ with $y$:
$x = \frac{1}{2}y + 1$
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:
$x -\frac{1}{2}y = 1$
Subtract $x$ from each side of the equation to isolate the $y$ term:
$-\frac{1}{2}y = - x + 1$
Divide each side by $-\frac{1}{2}$ to solve for $y$, which means we multiply by the reciprocal, which is $-2$:
$y = - x(-2) + 1(-2)$
Multiply out terms to simplify:
$y = 2x - 2$
