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Old 21st January 2012, 04:40 PM   #1 (permalink)
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H2 math questions, pls help!

Hi all! i have a lot of questions you probably can't spend your time answering all but i hope you can answer some of them .___.

1. http://i1088.photobucket.com/albums/...4/IMG_2141.jpg (was able to do everything except finding of the range of the composite function. usually range is found by double arrow method, which usually requires drawing of the graph to see the range, however, in this qn it's impossible to find the equation of g^-1 , so how to do? ) .

2. http://i1088.photobucket.com/albums/...4/IMG_2150.jpg (only unsure about second part, first part answer not needed - i was thinking if u wanna make use fo the first part, u needa sub in '2r' in the summation of (r+1)2^r right? -->>> which will become (2r+1)2^2r. however they want the summation of (2r+1)2^r, so my problem lies in the 2^2r part. how do i make 2^2r become 2^r?).

3. http://i1088.photobucket.com/albums/...4/IMG_2159.jpg ( only dunno how to do the last part. i was thinking, sub in 'n-1' in the first summation to get the summation that the question asked for. problem lies in the 'n^2' in the denominator. it should become (n-1)^2, so how to make it become n^2?)

4. http://i1088.photobucket.com/albums/...4/IMG_2160.jpg (problem lies in the very last part, "find an expression for f^-1(x) corresponding to each of the domains for f." ANS. TO THIS QN for previous parts (shown as qn3 on the answer book): http://i1088.photobucket.com/albums/...4/IMG_2161.jpg ) .

5. http://i1088.photobucket.com/albums/...4/IMG_2173.jpg
http://i1088.photobucket.com/albums/...4/IMG_2175.jpg

(first link consists of question and conjecture. conjecture is (n+1)! . but this is abit weird because there is an addition of '1' to the summation. second link shows the induction part, where S(k+1)=Sk+T(k+1). my question is, does T(k+1) = (k+1)(k+1)! or (k+1)(k+1)! +1 ? according to the answer it is the former, however i think it should be the latter).

6. http://i1088.photobucket.com/albums/...4/IMG_2176.jpg
doubtful about this formula cuz it wasn't taught to me. is the book correct? they also said use this to find the inverse of a composite function, but why would this be required?

7. http://i1088.photobucket.com/albums/...4/IMG_2177.jpg
referring to 'practice 3,' they say fourth term is equals to 16/25 of the 2nd term. so is it T2=(16/25)T4 or T4=(16/25)T2? the book says it is the latter, however i think it is the former.



sorry for so many questions! please help for anything if u can, thank u so much!

.

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Old 21st January 2012, 05:53 PM   #2 (permalink)
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Re: H2 math questions, pls help!

Cleared up the first 3 for you-see below:



Hope this helps. Peace.

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Old 21st January 2012, 11:06 PM   #3 (permalink)
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Re: H2 math questions, pls help!

Settle Q4 for you first:
(Note that completing the square is required to find your two f^-1(x) functions)


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Old 21st January 2012, 11:11 PM   #4 (permalink)
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Re: H2 math questions, pls help!

For 5, T(k+1) merely arises from the summation part; the constant value of 1 in front is merely a spectator and will not be involved. Solution is right.

For 6, book is right. This is something you should know, I am not sure why you mentioned you never saw this previously.

To find (fg)^-1 , sometimes after getting the expression for fg it might seem difficult (or impossible ) to obtain its inverse. However, you can simply find the expressions for f^-1 and g^-1 separately, and then embed g^-1 within f^-1, ie g^-1 f ^-1. You will still get (fg)^-1.


Last edited by whitecorp; 21st January 2012 at 11:16 PM.
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Old 21st January 2012, 11:28 PM   #5 (permalink)
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Re: H2 math questions, pls help!

For 7, it is the latter which is right, ie T4=16/25 *T2. Following the phrasing of the sentence in the question: the fourth term is 16/25 times that of the second term.

Hope this helps. Peace.

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Old 22nd January 2012, 09:46 AM   #6 (permalink)
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Re: H2 math questions, pls help!

To help clarify your doubt for Q6, I have done up the proof provided below:



If there is something you don't know, just ask. That is how you learn.The worst thing a student can do is to pretend he/she knows what is going on when everything is actually a blur.

Happy CNY. Peace.

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Old 22nd January 2012, 03:42 PM   #7 (permalink)
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Re: H2 math questions, pls help!

thanks so much whitecorp!

btw can Dfg=Dg be used in any other area besides that? like if they ask for the domain of a composite function, should i use that formula ; or find use the range fo the composite function, then look at the graph, then find the domain? my school taught me the second method.

and then for the 1st question, actually the [part i din't know how to do is part iii. i mean it is impossible to find g^-1(x), so how to find the range of the com[posite function?

i hope u can help again, thank u so much!

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Old 23rd January 2012, 02:20 PM   #8 (permalink)
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Re: H2 math questions, pls help!

Originally Posted by blacktoast94 View Post
thanks so much whitecorp!

btw can Dfg=Dg be used in any other area besides that? like if they ask for the domain of a composite function, should i use that formula ; or find use the range fo the composite function, then look at the graph, then find the domain? my school taught me the second method.
If you are finding the domain of the composite function, typically the first method is good enough, and in most cases it is actually less tedious.

Originally Posted by blacktoast94 View Post
and then for the 1st question, actually the [part i din't know how to do is part iii. i mean it is impossible to find g^-1(x), so how to find the range of the com[posite function?

i hope u can help again, thank u so much!

I did up the whole solution from (i) to (iv) for this question and posted it on my site:
http://www.whitegroupmaths.com/2012/01/functions.html see Q1. Hope it helps. Peace.

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