The function f is defined by \(f : x \mapsto x^2 + 4x\) for \(x \geq c\), where \(c\) is a constant. It is given that \(f\) is a one-one function.

(i) State the range of \(f\) in terms of \(c\) and find the smallest possible value of \(c\).

The function \(g\) is defined by \(g : x \mapsto ax + b\) for \(x \geq 0\), where \(a\) and \(b\) are positive constants. It is given that, when \(c = 0\), \(gf(1) = 11\) and \(fg(1) = 21\).

(ii) Write down two equations in \(a\) and \(b\) and solve them to find the values of \(a\) and \(b\).