8 The function f is defined by \(\mathrm { f } ( x ) = 3 x + 1\) for \(x \leqslant a\), where \(a\) is a constant. The function g is defined by \(\mathrm { g } ( x ) = - 1 - x ^ { 2 }\) for \(x \leqslant - 1\).
- Find the largest value of \(a\) for which the composite function gf can be formed.
For the case where \(a = - 1\),
- solve the equation \(\operatorname { fg } ( x ) + 14 = 0\),
- find the set of values of \(x\) which satisfy the inequality \(\operatorname { gf } ( x ) \leqslant - 50\).