Determine the equation of the inverse function f⁻¹(x) from the graph (Figure 4.21).

The graph shows a straight line labeled $f^{-1}$ passing through the points $(0,-2)$ and $(4,0)$.
The general equation for a straight line is $y = mx + c$.
Calculate the slope $m$:

$$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - (-2)}{4 - 0} = \frac{2}{4} = \frac{1}{2}$$

The y-intercept $c$ is the y-coordinate when $x=0$, which is $-2$.
Therefore, the equation of the inverse function is:

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

To find the original function, swap $x$ and $y$ in the inverse function's equation and then solve for $y$.
Let $y = f^{-1}(x)$, so $y = \frac{1}{2}x - 2$.
Swap $x$ and $y$:

$$x = \frac{1}{2}y - 2$$

Add 2 to both sides:

$$x + 2 = \frac{1}{2}y$$

Multiply both sides by 2:

$$2(x + 2) = y$$ $$y = 2x + 4$$

So, the equation of the function is:

$$f(x) = 2x + 4$$

The equations are:
Function: $\boxed{f(x) = 2x + 4}$
Inverse function: $\boxed{f^{-1}(x) = \frac{1}{2}x - 2}$