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Functions help

I need help with part a)
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Reply 1
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Vorsah
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Any1?
Reply 2
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Vorsah
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Is this the domain?
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Reply 3
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Vorsah
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Or should it be x is an element of (|R)^2 : x>0
(edited 9 years ago)
Reply 4
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Vorsah
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My final answer for part a), can some1 check this please?
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Original post by Vorsah
My final answer for part a), can some1 check this please?


x,y are in R, not R^2

Why can't -1, for example, be part of the domain?
Reply 6
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Original post by ghostwalker
x,y are in R, not R^2

Why can't -1, for example, be part of the domain?


So is the answer this?

Also what would your method be to find the range and domain for this type of question? I just want to compare your method to mine
(edited 9 years ago)
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Original post by Vorsah
So is the answer this?

Also what would your method be to find the range and domain for this type of question? I just want to compare your method to mine


Agree with the domain.

I'd rearrange and make y a function of x.

Your range is going to be a subset of B, so it can't be the whole of R, even leaving out "1".
Reply 8
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Hasufel
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you can tell straight away from the equation that x is not zero, y is not zero, because, if you then re-arrange and solve for y you get:

y=±∣x∣2x2+1\displaystyle y= \pm \frac{|x|}{\sqrt{2x^{2}+1}} for what y values does this exist? (according to the given info and what you`ve already worked out)

This together with the given info should point to the answer.

`Smore obvious than you think.
(edited 9 years ago)
Reply 9
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Original post by ghostwalker
Agree with the domain.

I'd rearrange and make y a function of x.

Your range is going to be a subset of B, so it can't be the whole of R, even leaving out "1".


Is it 0<y<1 ?
(edited 9 years ago)
Original post by Vorsah
Is it 0<y<1 ?



do what ghostwalker has suggested, then examine the behaviour of the +ve y function for large x (+ve and -ve)

(what limit does it approach?)

(you already know, from the Qn, that y is not negative)
(edited 9 years ago)
Reply 11
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Original post by Hasufel
do what ghostwalker has suggested, then examine the behaviour of the +ve y function for large x (+ve and -ve)

(what limit does it approach?)

(you already know, from the Qn, that y is not negative)


Is 0<y< 1/(sqrt2) ?
Original post by Vorsah
Is 0<y< 1/(sqrt2) ?


BINGO! :smile:
Reply 13
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Vorsah
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Original post by Hasufel
BINGO! :smile:


Thank you, can you help me with part c) ?
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Original post by Vorsah
Thank you, can you help me with part c) ?


What can't you do with part c)? Hasufel has virtually done that for you in post #9.
Reply 15
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Original post by ghostwalker
What can't you do with part c)? Hasufel has virtually done that for you in post #9.


Is this correct?
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Original post by Vorsah
Is this correct?


x goes to "+/-" isn't a function. It can only have one value.
Reply 17
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Original post by ghostwalker
x goes to "+/-" isn't a function. It can only have one value.


Is this correct?

Also why is there a modulus sign in Hasufel's answer?
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Original post by Vorsah
Is this correct?

If x<0, then that would make y<0, which it can't be, and that's why there's a modulus sign in Hasufel's answer.
Reply 19
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Original post by ghostwalker
If x<0, then that would make y<0, which it can't be, and that's why there's a modulus sign in Hasufel's answer.


thank you

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