Answer
$f^{-1}(x)=\dfrac{5-x}{3x}$
Work Step by Step
The given function, $
f(x)=\dfrac{5}{3x+1}
,$ is equivalent to
\begin{array}{l}\require{cancel}
y=\dfrac{5}{3x+1}
\
.\end{array}
Interchanging the $x$ and $y$ variables, and then solving for $y$ result to
\begin{array}{l}\require{cancel}
x=\dfrac{5}{3y+1}
\\\\
x(3y+1)=5
\\\\
3xy+x=5
\\\\
3xy=5-x
\\\\
y=\dfrac{5-x}{3x}
.\end{array}
Hence, the inverse function is $
f^{-1}(x)=\dfrac{5-x}{3x}
$.
