Answer
one-to-one function
inverse: $f^{-1}(x)=-4x-32$
Work Step by Step
Some of the ordered pairs of the given function, $
f(x)=-\dfrac{1}{4}x-8
$, are $
\left\{(-8,6)(-4,-7),(0,-8),(4,-9),(8,-10),...\right\}
$. Note that every $y$-coordinate from this function is unique. Hence, the given function is a one-to-one function.
To find the inverse, let $y=f(x)$. Then, interchange the $x$ and $y$ variables and solve for $y$. That is,
\begin{align*}
y&=-\dfrac{1}{4}x-8
\\&\Rightarrow
x=-\dfrac{1}{4}y-8
&(\text{interchange $x$ and $y$})
\\\\&
x+8=-\dfrac{1}{4}y
&(\text{solve for $y$})
\\\\&
(-4)(x+8)=\left(-\dfrac{1}{4}y\right)(-4)
\\\\&
-4x-32=y
\\&
y=-4x-32
.\end{align*}
Hence, the inverse is $
f^{-1}(x)=-4x-32
$.
