6. $$\mathrm { f } ( x ) = \frac { a x + b } { x + 2 } ; \quad x \in \mathbb { R } , x \neq - 2$$ where \(a\) and \(b\) are constants and \(b > 0\) ．
（a）Find \(f ^ { - 1 } ( x )\) ．
（b）Hence，or otherwise，find the value of \(a\) so that \(\operatorname { ff } ( x ) = x\) ． The curve \(C\) has equation \(y = \mathrm { f } ( x )\) and \(\mathrm { f } ( x )\) satisfies \(\mathrm { ff } ( x ) = x\) ．
（c）On separate axes sketch
（i）\(y = \mathrm { f } ( x )\) ，
（ii）\(y = \mathrm { f } ( x - 2 ) + 2\) ． On each sketch you should indicate the equations of any asymptotes and the coordinates，in terms of \(b\) ，of any intersections with the axes． The normal to \(C\) at the point \(P\) has equation \(y = 4 x - 39\) ．The normal to \(C\) at the point \(Q\) has equation \(y = 4 x + k\) ，where \(k\) is a constant．
（d）By considering the images of the normals to \(C\) on the curve with equation \(y = \mathrm { f } ( x - 2 ) + 2\) ，or otherwise，find the value of \(k\) ．