After a tumultuous week of near-death experience and some bizarre wrist-slitting, Miss Loi is utterly shocked by the realization that the last A-Maths question was posted almost a month ago on this blog!
So in order to appease the upmarket segment of A-Maths students and LMBFH Syndrome sufferers, here’s one of those irritating composite functions questions that have been appearing repeatedly in the actual O-Level exams (Paper 1 & 2) for the past few years.
The functions f and g are defined by
f(x) = 2√x, x > 0,
g(x) = x − 2, x > 2
Express each of the following in terms of f and g only.
- x → x − 4, x > 2
- x →
, x > 2 - x →
, x > 2
Miss Loi always tells her students not to anyhow whack, stay calm and know thy approach before attempting each question.
But there’re always exceptions to the rule. So when you see something like the above, guys ‘n gals, it’s Anyhow Whack Time!
Before you start taking out all your religious artifacts and start chanting in the exam hall, do remember that it’s not all about randomly trying out your fg, gf, f2, g2, f-1, g-1, f-1g, g-1f, f-1f, g-1g …
NOTE:
As the sagely saying goes “Anyhow whack also must whack smartly!“, please look at each final expression in the question:
- If it looks a little similar to f(x) or g(x) then trying whacking fg, gf, f2, g2 first.
- If it looks drastically different from f(x) or g(x) e.g. part 3 of the question above, then there’s a high chance an inverse function f-1 and/or g-1 is involved.
- Don’t forget the possibility of making use of the answer from an earlier part too!
OK with all these in mind, happy whacking guys and gals!
