(i) To find the inverse function \(f^{-1}(x)\), start with \(y = 4 - 5x\).

Solve for \(x\):

\(y = 4 - 5x\)

\(5x = 4 - y\)

\(x = \frac{4-y}{5}\)

Thus, \(f^{-1}(x) = \frac{4-x}{5}\).

To find the intersection, set \(f(x) = f^{-1}(x)\):

\(4 - 5x = \frac{4-x}{5}\)

Multiply through by 5:

\(20 - 25x = 4 - x\)

\(20 - 4 = 25x - x\)

\(16 = 24x\)

\(x = \frac{2}{3}\)

Substitute back to find \(y\):

\(y = 4 - 5 \left( \frac{2}{3} \right) = \frac{2}{3}\)

So, the point of intersection is \(\left( \frac{2}{3}, \frac{2}{3} \right)\).

(ii) The graph of \(y = f(x) = 4 - 5x\) is a straight line with a negative slope, intersecting the y-axis at 4.

The graph of \(y = f^{-1}(x) = \frac{4-x}{5}\) is also a straight line with a negative slope, intersecting the y-axis at \(\frac{4}{5}\).

The line \(y = x\) is the line of symmetry between the function and its inverse.