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Mathematics: Post your doubts here!

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Hey ! Amm is math compolsury in cie ? Lol i know it is :cry: but still if i can do some other subjects instead of this math :( mental math will really make me mental please tell me what can i do :oops:
Why are you so afraid of mathematics?
It keeps our mind active and fresh.
Nothing is hard until you put your heart and all your grace in your work.
I would suggest you to take mathematics. No other suggestion from my side.
 
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Someone plz help me in this stupid confusing domain range chapter :/
If someone can help me understand ~Domain Range~ chapter and ~Vector Paper 3~ only, I would be really Thankful to him/her :/


Help needed!!!
I know that range of a function is the domain of the inverse function and vice versa but how to find domain in this question
part (iv) only
and PLZZ answer with deep knowledge ( I mean with more theory and working which is clearly understandable to solve rest of the questions):
Thanks and May Allah bless us all with knowledge and A/A*s in A Levels Ameen:)
View attachment 46644


kitkat <3 :P Angelina_25 shazmina fantastic girl Anyone :SSS
Plejj :'/
Here Rookaya did this. http://www.twiddla.com/1729925 Aly Emran
 
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Aly Emran
Part i) RANGE OF G INVERSE
Domain of g(x) = range of g inverse.
Domain of g(x) >= 4
Hence, Range of g inverse >=4
Part ii) DOMAIN OF G INVERSE
Range of g(x) = Domain of g inverse
First complete square :¬
- ( x - 4)^2 + 16 = g(x)
Now exchange g(x) with y.
y = - (x - 4)^2 +16
Now exchange x with y and vice-verse.
x = -(y - 4)^2 +16
Make y as subject.
y = 4 + root (16 - x)
Now exchange y with g inverse.
So g inverse is 4 + root (16 - x)
Now for g inverse, any value of x >= 16 will have undefined answer, yeah? so x <= 16
Another way is :¬
Due to the minus sign, it is the maximum point on the graph. So x <= 16 is range of g(x) and according to Range of g(x) = Domain of g inverse, domain of g inverse is x <= 16

Hope you got it.
 
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Why are you so afraid of mathematics?
It keeps our mind active and fresh.
Nothing is hard until you put your heart and all your grace in your work.
I would suggest you to take mathematics. No other suggestion from my side.
Actually i would love to learn something im not good at but the problem is that i study by myself so maths cant be done without tutor thats why i asked .
 
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Oh Brillient (y)
got it :D
but cant we find the mid point and see that is the graph a min or max and then decide greater then and less than?
Ps: Is it necessary to do inverse of g(x) in part 1?? because part 2 demands inverse so the examiner might not accept the inverse answer of part 1 i guess :/
plzz help me on this issue too :)
Thanks in advance :)
No its not like that, till I know.
Go to this site :- http://www.examsolutions.net/maths-revision/syllabuses/CIE/period-1/P1/module.php 2 chapter is function. :)
Everything in it. :)
All the best. ^_^
 
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Not much with it! Saved answer here :¬
complex-png.21999

As the question states that the argument of z is least, z must represent the lowest possible point in the shaded region. Draw a tangent from the center to the lowest point on the circle (this doesn't have to be accurate) as shown by the blue line. This line represents |z|. The angle between the radius and the tangent is always 90 so a right-angled triangle is formed. The opposite side, with is equal to the radius is 1 unit. The magnitude of complex u is the hypotenuse and the adjacent represents |z|. you can easily find |u|, √(2^2+2^) = √8.
So, |z| =√(√8)^2 -1^2 = √8-1 =√7
 
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Not much with it! Saved answer here :¬
complex-png.21999

As the question states that the argument of z is least, z must represent the lowest possible point in the shaded region. Draw a tangent from the center to the lowest point on the circle (this doesn't have to be accurate) as shown by the blue line. This line represents |z|. The angle between the radius and the tangent is always 90 so a right-angled triangle is formed. The opposite side, with is equal to the radius is 1 unit. The magnitude of complex u is the hypotenuse and the adjacent represents |z|. you can easily find |u|, √(2^2+2^) = √8.
So, |z| =√(√8)^2 -1^2 = √8-1 =√7

thank you very much for ur explanations ~
 
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