Question

find the inverse of $f(x) = -\frac{1}{2}x + 7$

Explanation:

Step1: Replace $f(x)$ with $y$

$y = -\frac{1}{2}x + 7$

Step2: Swap $x$ and $y$

$x = -\frac{1}{2}y + 7$

Step3: Isolate the term with $y$

$x - 7 = -\frac{1}{2}y$

Step4: Solve for $y$

$y = -2(x - 7) = -2x + 14$

Step5: Replace $y$ with $f^{-1}(x)$

$f^{-1}(x) = -2x + 14$

Answer:

$f^{-1}(x) = -2x + 14$