It is now given that \(f(x) = \frac{-x}{\sqrt{4-x^2}}\) where \(-2 < x < 2\).

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

The function \(g\) is defined by \(g(x) = 2x\) for \(-a < x < a\), where \(a\) is a constant.

(c) State the maximum possible value of \(a\) for which \(fg\) can be formed.

(d) Assuming that \(fg\) can be formed, find and simplify an expression for \(fg(x)\).