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# Maths C3 - Functions... Help?

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1. Can someone please explain this example to me?
I've done all the previous sections to this from the Edexcel C3 Modular Maths textbook but this part honestly doesn't make sense to me
2. (Original post by Philip-flop)
Can someone please explain this example to me?
I've done all the previous sections to this from the Edexcel C3 Modular Maths textbook but this part honestly doesn't make sense to me

nm(x) means you take the function of m and substitute it into the function of n.
3. (Original post by RDKGames)

nm(x) means you take the function of m and substitute it into the function of n.
Oh right. Starting to understand a bit better now. But I think I don't really understand what the question is asking. Where is the p function answer for the first question?
4. Also I'm confused as surely substituting m(x)=1/x into 2/x+4 will be ?
5. Seriously, what exactly is the question asking to do.

I worked through Example 7 and it completely made sense but working through Example 8 it's almost like I've missed a chunk of knowledge from somewhere?
6. (Original post by Philip-flop)
Oh right. Starting to understand a bit better now. But I think I don't really understand what the question is asking. Where is the p function answer for the first question?
It's just saying that throughout the following questions express them in terms of m(x), n(x) and p(x) where ever they may be applicable. Doesn't necessarily mean they all go into a single question.

(Original post by Philip-flop)
Also I'm confused as surely substituting m(x)=1/x into 2/x+4 will be ?
You're not subbing it into 2/x + 4 you are subbing it into 2x+4.

2/x + 4 is not a stated function.
7. (Original post by RDKGames)
It's just saying that throughout the following questions express them in terms of m(x), n(x) and p(x) where ever they may be applicable. Doesn't necessarily mean they all go into a single question.

You're not subbing it into 2/x + 4 you are subbing it into 2x+4.

2/x + 4 is not a stated function.
Sorry I was being stupid again. I didn't realise what the question was asking exactly. I don't have to use all of the functions m(x),n(x) and p(x) to make up the equation 2/x+4 do I? just m(x) and n(x)?

Edit: After looking back at your answer, I understand now. Thank you so much!! I didn't realise we were allowed to pick and choose out of m(x),n(x) and p(x).

Seriously thanks for being patient and giving me your own time to help
8. For part b what is an indication that you need to complete the square?
9. (Original post by Philip-flop)
For part b what is an indication that you need to complete the square?
Because when you look at the functions given, the overall function cannot be m(x) because it's not a reciprocal function, and it cannot be n(x) because it's not a linear function. It only leaves you with p(x). In that function there is no term, thus implying the completion of the square.
10. (Original post by RDKGames)
Because when you look at the functions given, the overall function cannot be m(x) because it's not a reciprocal function, and it cannot be n(x) because it's not a linear function. It only leaves you with p(x). In that function there is no term, thus implying the completion of the square.
Oh yeah, of course. Because 4x^2+16x+14 is a quadratic equation the 4x^2 part of the quadratic sort of hints that p(x) is one of the functions to use as it is the only function with a x^2? Is that what you're saying?
11. (Original post by Philip-flop)
Oh yeah, of course. Because 4x^2+16x+14 is a quadratic equation the 4x^2 part of the quadratic sort of hints that p(x) is one of the functions to use as it is the only function with a x^2? Is that what you're saying?
Yes. It's a quadratic and p(x) is the only quadratic function so they must go together.

Once you're comfortable with that decision, you should notice that completion of the square is the only way to get it into that form of p(x); ie (something)2 - 2
12. This kind of question is weird and to my knowledge I've not seen it in an Edexcel C3 past paper (not to say that it can't be tested..)

The key is to understand how composite functions (i.e function of a function) work and once you're fine with what the question is asing, it's just trial and error/inspection.
13. (Original post by RDKGames)
Yes. It's a quadratic and p(x) is the only quadratic function so they must go together.

Once you're comfortable with that decision, you should notice that completion of the square is the only way to get it into that form of p(x); ie (something)2 - 2
Ok now I'm being even more stupid. When I complete the square I get...

I know is the same as but how come the way I've learnt to complete the square comes out as a completely different arrangement?
I'm actually having doubts as to whether to complete Maths at A2 if I can't even complete the square anymore
14. (Original post by SeanFM)
This kind of question is weird and to my knowledge I've not seen it in an Edexcel C3 past paper (not to say that it can't be tested..)

The key is to understand how composite functions (i.e function of a function) work and once you're fine with what the question is asing, it's just trial and error/inspection.
Yes I really hope questions on functions don't get laid out like this otherwise I will screw up
15. (Original post by Philip-flop)
Oh yeah, of course. Because 4x^2+16x+14 is a quadratic equation the 4x^2 part of the quadratic sort of hints that p(x) is one of the functions to use as it is the only function with a x^2? Is that what you're saying?
A lot of students find this type of question hard. But what you've said here is the thought process you need i.e. inspection/logic/trial and error.

So e.g. for b) you notice that to get a quadratic you can put into . And you try it and it works.

But there's no "completing the square" here. Completing the square means put into the form .

For c), it's easy to see that won't be involved so it's a case of trying different compositions of and .
16. (Original post by Philip-flop)
...
Different arrangement? How?

In the end it doesn't matter about arrangement, you still have completed the square successfully and correctly. Anything beyond that is just an extra.
17. (Original post by Philip-flop)
Ok now I'm being even more stupid. When I complete the square I get...

I know is the same as but how come the way I've learnt to complete the square comes out as a completely different arrangement?
I'm actually having doubts as to whether to complete Maths at A2 if I can't even complete the square anymore
I can see that you know how to complete the square.

For this question, you don't need to complete the square.
18. (Original post by RDKGames)
Then how would you do it?
You have a choice of only 3 functions you can use. It is clear that won't be involved.

To get something that starts with , experience with composing functions tells us that putting into will achieve this.

So we try and notice that we're done.

I think that most students who try to complete the square will do the same thing as the OP and get stuck.
19. Thank you guys. This is definitely a topic that I will have to keep coming back to in the future to reimburse my understanding! I will be attempting Exercise 2D now as I'm hoping to finish the rest of this chapter by the end of the week

(Original post by notnek)
A lot of students find this type of question hard. But what you've said here is the thought process you need i.e. inspection/logic/trial and error.

So e.g. for b) you notice that to get a quadratic you can put into . And you try it and it works.

But there's no "completing the square" here. Completing the square means put into the form .

For c), it's easy to see that won't be involved so it's a case of trying different compositions of and .
I'm glad I'm not the only student who finds this type of question difficult. I'm hoping with more practice my understanding will become a lot clearer!!

How do I know what kind of functions I need to mix and match if I don't complete the square of the quadratic first?

(Original post by RDKGames)
Different arrangement? How?

In the end it doesn't matter about arrangement, you still have completed the square successfully and correctly. Anything beyond that is just an extra.
Thank you. At least I managed to actually get 'completing the square' right, so that's something aha :P
As you can tell I'm not exactly a natural at Maths but will keep trying my best to power through the subject and hopefully come out with a half decent grade by the end of it (along with all the luck I can get of course!!).
20. (Original post by Philip-flop)
How do I know what kind of functions I need to mix and match if I don't complete the square of the quadratic first?
There's only 3 functions to choose from and doesn't fit with the question.

So you can try composing and and see what happens.

It's much more useful to try this question yourself instead of looking at the example solution. The solution doesn't really explain the thought process.

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