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Composite Functions - Could anyone please help? watch
Last edited by Sam00; 13-11-2015 at 15:44.
- 13-11-2015 14:17
(Original post by Sam00)
- 13-11-2015 15:33
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?
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.
BTW in future you will be better posting in the maths academic help area to get better/quicker replies.