Functions f and g are defined by

\(f(x) = x + \frac{1}{x}\) for \(x > 0\),

\(g(x) = ax + 1\) for \(x \in \mathbb{R}\),

where \(a\) is a constant.

(a) Find an expression for \(gf(x)\).

(b) Given that \(gf(2) = 11\), find the value of \(a\).

(c) Given that the graph of \(y = f(x)\) has a minimum point when \(x = 1\), explain whether or not \(f\) has an inverse.

It is given instead that \(a = 5\).

(d) Find and simplify an expression for \(g^{-1}f(x)\).

(e) Explain why the composite function \(fg\) cannot be formed.