Determine the equation of the function from the graph.

The graph shows a straight line passing through the origin $(0,0)$ and the point $(3,1)$.
The general equation for a straight line is $y = mx + c$, where $m$ is the slope and $c$ is the y-intercept.
Calculate the slope $m$:

$$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 0}{3 - 0} = \frac{1}{3}$$

Since the line passes through $(0,0)$, the y-intercept $c$ is 0.
Therefore, the equation of the function is:

$$y = \frac{1}{3}x$$

To find the inverse function, swap $x$ and $y$ in the original function's equation and then solve for $y$.
Original function: $y = \frac{1}{3}x$
Swap $x$ and $y$: $x = \frac{1}{3}y$
Multiply both sides by 3 to solve for $y$:

$$3x = y$$

So, the equation of the inverse function is:

$$y = 3x$$

The equations are:
Function: $\boxed{y = \frac{1}{3}x}$
Inverse function: $\boxed{y = 3x}$