f(x) = (ax + b) / (x + 2 ); x ∈ R, x ≠ -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 ff(x) = x.
The curve C has equation y = f(x) and f(x) satisfies ff(x) = x.
(c) On separate axes sketch
(i) y = f(x),
(ii) y = 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 Cat the point P has equation y = 4x - 39. The normal to C at the point Q has equation y = 4x + k , where k is a constant.
(d) By considering the images of the normals to C on the curve with equation y = f(x - 2) + 2, or otherwise, find the value of k.