Functions f and g are defined as follows:

\(f : x \mapsto x^2 + 2x + 3\) for \(x \leq -1\),

\(g : x \mapsto 2x + 1\) for \(x \geq -1\).

(a) Express \(f(x)\) in the form \((x+a)^2 + b\) and state the range of \(f\).

(b) Find an expression for \(f^{-1}(x)\).

(c) Solve the equation \(gf(x) = 13\).