Answer
$f^{-1}(x)=\dfrac{7-4x}{2x}$
Work Step by Step
The given function, $
f(x)=\dfrac{7}{2x+4}
,$ is equivalent to
\begin{array}{l}\require{cancel}
y=\dfrac{7}{2x+4}
\
.\end{array}
Interchanging the $x$ and $y$ variables, and then solving for $y$ result to
\begin{array}{l}\require{cancel}
x=\dfrac{7}{2y+4}
\\\\
x(2y+4)=7
\\\\
2xy+4x=7
\\\\
2xy=7-4x
\\\\
y=\dfrac{7-4x}{2x}
.\end{array}
Hence, the inverse function is $
f^{-1}(x)=\dfrac{7-4x}{2x}
$.
