Answer
Hence, the inverse is $
f^{-1}(x)=\dfrac{x-4}{2}
$.
Work Step by Step
Some of the ordered pairs of the given function, $
f(x)=2x+4
$, are $
\left\{(-2,0)(-1,2),(0,4),(1,6),(2,8),...\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*}\require{cancel}
y&=2x+4
\\&\Rightarrow
x=2y+4
&(\text{interchange $x$ and $y$})
\\&
x-4=2y
&(\text{solve for $y$})
\\\\&
\dfrac{x-4}{2}=\dfrac{\cancel2y}{\cancel2}
\\\\&
\dfrac{x-4}{2}=y
\\\\&
y=\dfrac{x-4}{2}
.\end{align*}
