Functions f and g are defined by

\(f(x) = 4x - 2, \text{ for } x \in \mathbb{R},\)

\(g(x) = \frac{4}{x+1}, \text{ for } x \in \mathbb{R}, x \neq -1.\)

(a) Find the value of \(fg(7)\).

(b) Find the values of \(x\) for which \(f^{-1}(x) = g^{-1}(x)\).