Answer
$f^{-1}(x)=\dfrac{5}{3x}-\dfrac{1}{3}$
Work Step by Step
$f(x)=\dfrac{5}{3x+1}$
Replace $f(x)$ with $y$:
$y=\dfrac{5}{3x+1}$
Interchange $x$ and $y$:
$x=\dfrac{5}{3y+1}$
Solve for $y$. Begin by taking $3y+1$ to multiply the left side:
$(3y+1)x=5$
Take $x$ to divide the right side:
$3y+1=\dfrac{5}{x}$
Take the $1$ to the right side:
$3y=\dfrac{5}{x}-1$
Take the $3$ to divide the right side:
$y=\dfrac{5}{3x}-\dfrac{1}{3}$
Replace $y$ with $f^{-1}(x)$:
$f^{-1}(x)=\dfrac{5}{3x}-\dfrac{1}{3}$
