#### Answer

$f^{-1}(x)= \frac{1}{2}(3x-1)$

#### Work Step by Step

We are given:
$f(x)=\frac{2x+1}{3}$
To find the inverse function, we switch $x$ and $y$ and solve for $y$:
$y=\frac{2x+1}{3}$
$x=\frac{2y+1}{3}$
$3x=2y+1$
$3x-1=2y$
$y=\frac{1}{2}(3x-1)$
Thus the inverse is:
$f^{-1}(x)= \frac{1}{2}(3x-1)$