user20031516
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How do I express the compositefunction pq in the form pq(x)...

P(x) = x+1/x-2
Q(x) = 2x+1/x-1
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ghostwalker
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(Original post by user20031516)
How do I express the compositefunction pq in the form pq(x)...

P(x) = x+1/x-2
Q(x) = 2x+1/x-1
pq(x) = p(q(x))

Since p(x)=\dfrac{x+1}{x-2}, I assume - you've not put any brackets in.

Then p(q(x)) = \dfrac{q(x)+1}{q(x)-2}

and substitute for q(x) and simplify.

In summary, you're just replacing x with q(x) in the definition of p(x).
Last edited by ghostwalker; 9 months ago
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user20031516
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(Original post by ghostwalker)
pq(x) = p(q(x))

Since p(x)=\dfrac{x+1}{x-2}, I assume - you've not put any brackets in.

Then p(q(x)) = \dfrac{q(x)+1}{q(x)-2}

and substitute for q(x) and simplify.

In summary, you're just replacing x with q(x) in the definition of p(x).
I'm not sure I understand. Can you explain it a little more if you can?
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xipo7101
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https://www.examsolutions.net/tutori...=C3&topic=1372
Work through examples too.
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user20031516
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(Original post by xipo7101)
https://www.examsolutions.net/tutori...=C3&topic=1372
Work through examples too.
Thanks. Those are A-level but still useful
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xipo7101
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They love to link this topic with inverse functions so it is usually 6-12 marks. ( for my year was 12!!! a whole grade)
Inevrese functions: https://www.examsolutions.net/tutori...=C3&topic=1372 (do first 2 examples)
https://www.examsolutions.net/tutori...=C3&topic=1372 (8/9 grade questions they love to ask as a last part).
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ghostwalker
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(Original post by user20031516)
I'm not sure I understand. Can you explain it a little more if you can?
It is literally replace "q(x)" in that formula for p(q(x)) I gave, with the definition of q(x), and then simplify.

Have you not worked through/seen some examples before tackling this?
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user20031516
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(Original post by xipo7101)
They love to link this topic with inverse functions so it is usually 6-12 marks. ( for my year was 12!!! a whole grade)
Inevrese functions: https://www.examsolutions.net/tutori...=C3&topic=1372 (do first 2 examples)
https://www.examsolutions.net/tutori...=C3&topic=1372 (8/9 grade questions they love to ask as a last part).
Oh god that's a stupid amnt of marks. I'll brush up on it for sure, thank you
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user20031516
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(Original post by ghostwalker)
It is literally replace "q(x)" in that formula for p(q(x)) I gave, with the definition of q(x), and then simplify.

Have you not worked through/seen some examples before tackling this?
Yes I have done examples. Mainly though they'll be something like f(x)=2x+2, g(x)=x^2, which is obviously quite simple to sort out into gf(x), fg(x), whatever. Two fraction type values are tricky though and admittedly I have limited practise on it. Thanks for your help.
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