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Prelim 2016 Maths Help Thread (2 Viewers)

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eyeseeyou

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Okay I am very confused with this:
1. Find the inverse function f^-1(x) of each function and verify that f^-1(f(x))=f(f^-1(x))=x
a. f(x)=(x-2)^2, x is less than or equal to 2
b. f(x)=x(x+2), x is greater than or equal to 1
c. f(x)=(x-1)^2+2, x is greater than or equal to 1
 

davidgoes4wce

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Also suggest for any students in Year 11 and 12 taking 2 Unit and 3 Unit, get a copy of Warwick Marlin's formulae book for Year 11 and Year 12 (2 separate books), they are about 60 pages each book. It has every formula you need to remember for the course. (The cost is $10 per book and you can get it pretty much at any Dymocks store). Even when I do the questions , I have to time from time refer to the formula book, its also a good way of refreshing your memory on key concepts.

Here is a link to the books:

https://www.understandingmaths.com/catalog
 

davidgoes4wce

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I know in the HSC they now allow a formula sheet, but some of those formulas you do need to ROTE memorise as it will aid you in understanding the questions.
 

davidgoes4wce

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Also suggest for any students in Year 11 and 12 taking 2 Unit and 3 Unit, get a copy of Warwick Marlin's formulae book for Year 11 and Year 12 (2 separate books), they are about 60 pages each book. It has every formula you need to remember for the course. (The cost is $10 per book and you can get it pretty much at any Dymocks store). Even when I do the questions , I have to time from time refer to the formula book, its also a good way of refreshing your memory on key concepts.

Here is a link to the books:

https://www.understandingmaths.com/catalog
The books I specifically refer to for 3 Unit:

Facts and Formulas Year 11 Extension 1 (2&3 Unit)
ISBN: 9781875462216

and

Facts and Formulas Year 12 Extension 1 HSC
ISBN: 9781875462230
 

eyeseeyou

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The books I specifically refer to for 3 Unit:

Facts and Formulas Year 11 Extension 1 (2&3 Unit)
ISBN: 9781875462216

and

Facts and Formulas Year 12 Extension 1 HSC
ISBN: 9781875462230
How come there's no book for extension 2?
 

Trebla

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Okay I am very confused with this:
1. Find the inverse function f^-1(x) of each function and verify that f^-1(f(x))=f(f^-1(x))=x
a. f(x)=(x-2)^2, x is less than or equal to 2
b. f(x)=x(x+2), x is greater than or equal to 1
c. f(x)=(x-1)^2+2, x is greater than or equal to 1
Ok let's start with f(x)=(x-2)2 for x < 2. What did you get for the inverse function f-1(x)?
 

eyeseeyou

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Okay I am very confused with this:
1. Find the inverse function f^-1(x) of each function and verify that f^-1(f(x))=f(f^-1(x))=x
a. f(x)=(x-2)^2, x is less than or equal to 2
b. f(x)=x(x+2), x is greater than or equal to 1
c. f(x)=(x-1)^2+2, x is greater than or equal to 1
BUMP
 

Trebla

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Do I answer both your Questions Trebla or what?
Yes. That question you managed to answer yourself, what was the problem you had with it originally that prompted you to ask it?
 

eyeseeyou

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Yes. That question you managed to answer yourself, what was the problem you had with it originally that prompted you to ask it?
if you are referring the question with the cubic I think that problem was that I expanded it out by accident when I wasn't supposed to

BTW Trebla, you usually don't seem to help out a lot with the maths threads
 

eyeseeyou

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I'll try it here

y=(x-2)^2, x <_ 2
Switch x and y around
x=(y-2)^2, y <_ 2
Squareroot of x=y-2, x <_2
squareroot of x+2=y
y=squareroot of (x) +2
Given our condition is x <_2 we can only have one case

Okay wtf am I doing wrong

Get carrotsticks to help us out
 

InteGrand

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I'll try it here

y=(x-2)^2, x <_ 2
Switch x and y around
x=(y-2)^2, y <_ 2
Squareroot of x=y-2, x <_2
squareroot of x+2=y
y=squareroot of (x) +2
Given our condition is x <_2 we can only have one case

Okay wtf am I doing wrong

Get carrotsticks to help us out
You needed to take the negative square root, since y needed to be ≤ 2.
 
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