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Further Mathematics Paper 2, Nov/Dec. 2009  
Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Main
General Comments
Weakness/Remedies
Strength
Question 2

Given that f(x) = , g(x) =   ,  x  and h(x) = (x – 1, where x  R, the set of real numbers, find

  1. gof(x);
  2. the inverse of h(x).
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Observation

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.

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