(i) Given \(f(x) = 2x - 3\), we need to find \(ff(x)\).

First, calculate \(f(f(x)) = f(2x - 3) = 2(2x - 3) - 3 = 4x - 6 - 3 = 4x - 9\).

Set \(4x - 9 = 11\).

Solve for \(x\):

\(4x - 9 = 11\)

\(4x = 20\)

\(x = 5\)

(ii) Set \(f(x) = g(x)\):

\(2x - a = x^2 - 6x\)

Rearrange to form a quadratic equation:

\(x^2 - 8x + a = 0\)

For exactly one real solution, the discriminant must be zero:

\(b^2 - 4ac = 0\)

Here, \(b = -8\), \(a = 1\), \(c = a\).

\((-8)^2 - 4 \times 1 \times a = 0\)

\(64 - 4a = 0\)

\(4a = 64\)

\(a = 16\)