Kiroii: Thought Miss Loi's pic is all plastered over this website? Else, what kind of pic are you looking for you surreptitious old fogey?! LOL

There's no hard and fast rule for composite functions questions such as this that involves somewhat working backwards from given expressions.

Actually most of the time the expressions are not that complex (at least in the beginning of the question) and students should be able to 'see' at first glance and substitute in the right functions quickly.

If you're really worried and confused in the exam and need some standard 'steps', as written in this post, go through quickly the sequence of combos like fg, gf, f², g² as stated in this blog post. If you still don't get the intended expression work out the inverse and try out the combos of f^-1 and g^-1.

Also do be alert to the possibility of using any answer(s) from the previous part. E.g. refer to part 2 of this question.

f^-1 -------- y =2 √ x
x² / 4 = y

with g being x - 2

f^-1 g = [(x-2)²] /4

Yes when you see that the final expression looks a bit distant from your original f(x) and g(x), in this case there's a denominator, it's time to consider working out the inverse!

for number 3 is

...f^-1 g

2) is g²(f) Well done! You remembered to use the answer from part 1! i.e. by simply substituting f(x) into g²(x) you'll get 2√x - 4

3) thinking