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2. (Original post by Sam00)
I am revising composite functions but really can't get my head around it.

I under the f(x) part but have spent a long time trying to understand the g(x) part and how to find fg(x) and gf(x).

For example I know that if f(x) = x^2 - 3 then if I was finding the f(3) it would be 3(3) - 3 = 6.

i just don't understand where the g(x) fits into this, for example if g(x) = x + 2, how would I work out the fg(x) and the gf(x) taking into account the aforementioned values?
Okay I will help you out. f(x) means that you apply the function f to the value x. You seem to have no problem with this as you found f(3) with no issues. Now when you compose two functions what you are doing is applying one function and then with the value you get out apply the second function to that value. Now the order in which you apply the two functions doesn't necessarily give the same result. Hopefully an example will make this clear.

In your case we have f(x) = x^2 - 3 and g(x) = x + 2. Now we can make to compositions with these two functions namely f o g (this is the notation used and it means f composed with g) and g o f.

Taking f o g as an example:

f o g means we apply f to g that is f(g(x)). Now in your case you want to look at the composition f o g (3) that is the same as applying g to 3 then applying f to g(3) that is f(g(3)). Now g(3)=3+2=5 so f(g(3))=f(5)=5^2-3=25-3=22. So we conclude f o g (3)=22.

Now see if you can find out what (g o f)(3) is and compare that with (f o g)(3).

If you can do that then try and find what (f o g)(x) for any x in the domain of f. Then instead of applying g then f you can do it in one go.

Hopefully that is clear even if a little long winded and hopefully after a few examples it will become easier to you.

Good luck.

BTW in future you will be better posting in the maths academic help area to get better/quicker replies.

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