Although majority of the candidates attempted this question, most of them were reported to be unable to determine the composite function correctly. While some of them substituted g(x) into f(x), others could not manipulate the fractions correctly. Majority of them were also reported not to determine the inverse of h(x) correctly. In part (a), gof(x) = = .
This is the same as x = (x
In part (b), h(x) = (x – 1. But hoh-1(x) = x, i.e. (h-1(x) - 1 = x. This implied that h-1(x) – 1 = x2 or h-1(x) = x2 + 1.
, g(x) = 
, x 
and h(x) = (x – 1
, where x 
R, the set of real numbers, find
= 
.
x 
= 
(x 
. But hoh-1(x) = x, i.e. (h-1(x) - 1
= x. This implied that h-1(x) – 1 = x2 or h-1(x) = x2 + 1.