Question

multiple choice
what is the equation of the inverse of the following function?
$f(x) = -4x - 8$
a $f^{-1}(x) = \frac{1}{4}x + 8$
b $f^{-1}(x) = -\frac{1}{4}x - 2$
c $f^{-1}(x) = \frac{1}{4}x - 2$
d $f^{-1}(x) = -\frac{1}{4}x + 2$

Explanation:

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

$y = -4x - 8$

Step2: Swap $x$ and $y$

$x = -4y - 8$

Step3: Solve for $y$, isolate term with $y$

$x + 8 = -4y$

Step4: Solve for $y$, divide by $-4$

$y = -\frac{1}{4}x - 2$

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

$f^{-1}(x) = -\frac{1}{4}x - 2$

Answer:

B. $f^{-1}(x)=-\frac{1}{4}x - 2$