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#### melanie.dee

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##### Need help: URGENT !!! LOL!
« Reply #15 on: November 05, 2007, 02:58:05 pm »
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Quote from: "costargh"
Yeh thanks. I just went and did my own research on VCAA website and found same thing. Also take into account that my C's have been mid range C's (from memory) and not border line C's and I guess that from now until friday and monday I can only really go up... I just emailed my teacher. Hope she writes back over the long weekend lol...although I doubt it.

At least if I can get my C's up to a high C range or maybe even a C+ I will feel a lot more confident that I can get my 25!

Thanks heaps to everyone that has helped and advised me and stuff!

One question...

The function f: [a,∞) --> R with rule f(x) = 2(x-3)^2 + 1 will have an inverse function if

A. a ≤ -3
B. a ≥ -3
C. a ≥ 1
D. a ≤ 3
E.  a ≥ 3

explanation?

well taking into account im shit at methods and am aiming for 25 too haha.. therefore might be wrong

to have an inverse function, it must be 1:1 ie each x value corresponds to a single y value, and vice versa

seeing as that is a parabola

it can only have an inverse for like one half of it (if that makes sense haha. like split it through the minimum)

the equation tells you its been shifted 3 to the right (x-3) or you could even graph it if you need. there the x coordinate of the minimum or midway point is 3

they've defined the upper domain as inifinite.. therefore you need the right hand side of the parabola.. which starts at 3

therefore the answer is a > or equal to 3

----------------------

is that right? according to the answers? i could be wrong haha

#### costargh

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##### Need help: URGENT !!! LOL!
« Reply #16 on: November 05, 2007, 03:09:26 pm »
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Yep thats right
74% of people got that right. I still dont get why its only one half of the parabola (as you said)
=S
argh I feel dumb

#### melanie.dee

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##### Need help: URGENT !!! LOL!
« Reply #17 on: November 05, 2007, 03:39:58 pm »
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yeh but remember methods is a scewed population, you get people above the average sort of vce intelligence doing it, because those that arnt do further or no maths. so thats 74% of an already smart population.. so dont worry about it

anyway um do you get what i mean by 1:1? because for a parabola, a y value is going to correspond to two x values.. ie if you draw a horizontal line accross the graph, its going to hit the graph in 2 points.

for a graph to have an inverse, it CANT do that. it can only hit it in one point. therefore, for an inverse you need to work out what part of the graph gives you only a value of x for each y value. for a parabola, you simply cut it down the middle. both halves can have an inverse.

like for that one above you could have an inverse from neg infinity to 3, and then from 3 to positive infinity. yeh? except in the question they've already defined the upper boundary as positiv infinity.. therefore you know its the '3 to pos infinity' half of the of the graph.

do you get it kinda? im not sure how else to explain it. find the section on inverses in your text book

#### costargh

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##### Need help: URGENT !!! LOL!
« Reply #18 on: November 05, 2007, 03:47:41 pm »
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yeh i know what one to one function is and then OMG i just realised lol shitt i get it now lol... ok so if its a parabola just look at one half of the graph because their symmetrical and if you have both parts of the graph on the left and right of the turning point then when u draw a horizontal line it will cross twice meaning its not one to one.
OMG I BLOODY UNDERSTAND NOW!!! thank youuuuuuu omg seriously thank you. Quoted by Celine Dion " its all coming back to me"
heheh
thanks !

#### avogarbro

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##### Need help: URGENT !!! LOL!
« Reply #19 on: November 05, 2007, 04:30:50 pm »
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In my opinion costargh, you should have done accounting in year 11, instead of methods. Since you may have the capability to do better in year 12. I wish i did that.

#### costargh

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##### Need help: URGENT !!! LOL!
« Reply #20 on: November 06, 2007, 04:00:29 pm »
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Ive been doing a year ahead in maths since year 7 do it bas just a formality to do methods 3/4 in year 12. Didnt have the choice ( well i did...)