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Qualification => Subject Doubts => GCE AS & A2 Level => Math => Topic started by: °o.O-hash94-O.o° on May 02, 2011, 05:24:37 am

Title: Functions - P1 ions f
Post by: °o.O-hash94-O.o° on May 02, 2011, 05:24:37 am
can some give some help regarding the functions for p1...

the range, domain makes me really confused...
and especially the question in latest papers like finding the largest value for A for which function has inverse..

Title: Re: Functions - P1 ions f
Post by: Saavya on May 03, 2011, 10:10:11 am
same problem here
Title: Re: Functions - P1 ions f
Post by: Arthur Bon Zavi on May 04, 2011, 10:02:57 am
Sample question ?
Title: Re: Functions - P1 ions f
Post by: EMO123 on May 05, 2011, 05:54:46 pm
if anyone then the same Q
Title: Re: Functions - P1 ions f
Post by: Arthur Bon Zavi on May 05, 2011, 05:56:12 pm
if anyone then the same Q

Give a particular question.
Title: Re: Functions - P1 ions f
Post by: I Jimmy I on May 06, 2011, 11:38:24 am
I have the same doubt in every paper! I always guess with the "functions" question
Anyways lets try question 10 of MJ 09? :)
Title: Re: Functions - P1 ions f
Post by: Master_Key on May 06, 2011, 02:20:57 pm
I have the same doubt in every paper! I always guess with the "functions" question
Anyways lets try question 10 of MJ 09? :)

Use completed square form to answer 10(i).

Use the value of "b" from 10(i) to find the value of x. x+b=0. x=-b. A = 2x. You got your 10 (ii).

Finding range. Use the values of domain to find the minimum possible value. Use it to find maximum if you can or else just state Range= x>=The value you found as minimum. Your 10(iii).

10(iv) :- A function only has an inverse if it is one-one function.

10(v) Use completed square form of 10(i) to find an inverse of f(g).
Square root((x-c)/a) - b.

I hope you do some work to find answers as exams are near simply giving off answers will not help you so i thought to explain you the method and work yourself.
Title: Re: Functions - P1 ions f
Post by: I Jimmy I on May 06, 2011, 06:13:32 pm
Ok Im having trouble understanding part 2 and 3 of this question.

Q. State the value of A for which the graph of y=f(x) has a line of symmetry.
What does it mean exactly...?

And Im looking for a quick explanation on how to find the range and domain for any type of question.

Cheers if some1 can explain the above :)
Title: Re: Functions - P1 ions f
Post by: Arthur Bon Zavi on May 07, 2011, 08:00:20 am
Ok Im having trouble understanding part 2 and 3 of this question.

Q. State the value of A for which the graph of y=f(x) has a line of symmetry.
What does it mean exactly...?

And Im looking for a quick explanation on how to find the range and domain for any type of question.

Cheers if some1 can explain the above :)

When you bring down a function (equation) in the completed square form, you will get the answer in the form : a (x + b)2 + c

So the b which you get is the line of the symmetry.

For example if you got the square form as : a(x+b)2 + c, then :

x = -b is your line of symmetry. Note if c is negative, the symmetry is c = -(-b), making it x = b.

DOMAIN AND RANGE :

Normally, in a question about functions, you will be given EITHER domain (the values which x can take) of the function OR range (the value of the whole function) OR both.

You have normal function, you find it's range if domain is given or either way, or if both are given, take it !

Then you find it's inverse, so :

The range of inverse function will be achieved by placing the values of x from domain of the normal function.

The domain will be achieved by placing the values of x from range of the normal function.
Title: Re: Functions - P1 ions f
Post by: Arthur Bon Zavi on May 07, 2011, 08:17:54 am
Ok Im having trouble understanding part 2 and 3 of this question.

Q. State the value of A for which the graph of y=f(x) has a line of symmetry.
What does it mean exactly...?

And Im looking for a quick explanation on how to find the range and domain for any type of question.

Cheers if some1 can explain the above :)

You will get this as the answer when you do it in a square form : 2(x - 3)2 - 5
If you find the value of y by f(3), you will get y as -5. There the curve is bending so, forming a symmetry line which is x = 3
Now you know symmetry is exactly half so value of A will be 2(x) where value of x is 3.

Simply : 2 * 3 = 6

A = 6, so :

0 <= x <= 6
Title: Re: Functions - P1 ions f
Post by: elemis on May 07, 2011, 08:42:19 am
y = c is your line of symmetry. Note if c is negative, the symmetry is y = +(-c), making it y = -c.

That is incorrect. The equation of the line of symmetry is x = -b as per you illustrated example.
Title: Re: Functions - P1 ions f
Post by: Arthur Bon Zavi on May 07, 2011, 09:22:44 am
That is incorrect. The equation of the line of symmetry is x = -b as per you illustrated example.

My mistake. Sorry. Edited the post. ;D
Title: Re: Functions - P1 ions f
Post by: °o.O-hash94-O.o° on May 08, 2011, 12:13:38 pm
ok understood a little

here's another question...

m/j2010 paper 12
q11

part (ii) and (iii)

http://www.xtremepapers.me/CIE/International%20A%20And%20AS%20Level/9709%20-%20Mathematics/9709_s10_qp_12.pdf (http://www.xtremepapers.me/CIE/International%20A%20And%20AS%20Level/9709%20-%20Mathematics/9709_s10_qp_12.pdf)
Title: Re: Functions - P1 ions f
Post by: elemis on May 08, 2011, 01:10:56 pm
ok understood a little

here's another question...

m/j2010 paper 12
q11

part (ii) and (iii)

http://www.xtremepapers.me/CIE/International%20A%20And%20AS%20Level/9709%20-%20Mathematics/9709_s10_qp_12.pdf (http://www.xtremepapers.me/CIE/International%20A%20And%20AS%20Level/9709%20-%20Mathematics/9709_s10_qp_12.pdf)

The sketch would look like this (see below). Ignore any part of the curve to the left of the origin.

The graph is not defined for anything less than 1 or greater than 7.... draw a horizontal line at those points, notice they never intersect the curve.