Mathematics: Post your doubts here!

[Hassanmahmud]

Re: Maths made easy =) stuck sumwhere?Ask ur doubts here!!

Hi
I have doubt in maths paper 4 ( 580)may/june 2009
f(x)=2x-1 g(x)=x2+1 h(x)=2x means (2 power x)

a)find the value of
i) f(-1/2)
ii) g(-5)
iii) h(-3)

b)find the inverse of function f-1(x)
c)g(x)=z
Find x in term of z

d) find gf (x)in its simplest form


please explain me easy way and thanks

 

[abcde]

Re: Maths made easy =) stuck sumwhere?Ask ur doubts here!!

AOA! I couldn't resist solving this
For (a) part, you simply insert the values of x into the respective functions like this:
(i) f(-1/2) = 2(-1/2) - 1 = -1 -1 = -2
(ii) g(-5) = (-5)^2 + 1 = 25 +1 = 26.
(iii) h(-3) = 2^-3 = 1/2^3 = 1/8.

(b) Let y = 2x - 1.
=> x = (y+1)/2
Since f(x) = y, f-1 = x.
f-1 = (y+1)/2.
x and y are just dummy variables so you may write it like this: f-1(x) = (x +1)/2.

(c) g(x) = z.
=> x^2 + 1 = z
=> x^2 = z - 1
=> x = +/- underroot (z - 1).

(d) gf(x) = g(2x - 1) function f is inserted here
= (2x - 1)^2 + 1
= 4x^2 - 4x + 2.

I hope you understand.

 

[abcde]

Re: Maths made easy =) stuck sumwhere?Ask ur doubts here!!

AOA, math_angel!
I'm having some confusions regarding geometrical transformations: Why do we have to use the same scale for both the x and y axes when we draw the original figure and its image? What happens if the scale for both the axes is different? Secondly, under what circumstances is a NEGATIVE shear factor obtained? Kindly explain. I hope u can reply asap!! Jazakallah!

 

[jazzangel16]

Re: Maths made easy =) stuck sumwhere?Ask ur doubts here!!

Hey.. there was some formula sheet posted here.. I can't find it now.. can you give me the link please

 

[XPFMember]

Re: Maths made easy =) stuck sumwhere?Ask ur doubts here!!

AOA, math_angel!
under what circumstances is a NEGATIVE shear factor obtained? Kindly explain. I hope u can reply asap!! Jazakallah!

Waalaikumassalam!!

Formula for shear factor => dist. point moves due to shear/dist. of that point from invariant line

dist. point moves due to shear : always move from object to image now see if it is +ve or -ve (+ve is up or right movement and -ve is down or left movement)

dist. of that point from invariant line:always move from invariant line to the point now check whether its positive or negative then use calc. to find out final ans. putting signs appropriately

The same applies for stretch dont forget to go from invariant line to point

hope it's clear now!! remember sumtimes both values u put in the formula might cum as -ve hence ur s.f will finally be +ve

 

[XPFMember]

Re: Maths made easy =) stuck sumwhere?Ask ur doubts here!!

AOA! I couldn't resist solving this
For.....

Waalaikumassalam!! Well JazakAllah Khair...i was kinda busy + lazy to solve this

AOA, math_angel!
I'm having some confusions regarding geometrical transformations: Why do we have to use the same scale for both the x and y axes when we draw the original figure and its image? What happens if the scale for both the axes is different? I hope u can reply asap!! Jazakallah!

Waalaikumassalam! well...i never noticed this :| can u plz give sum example....btw who said it shud be the same scale...just put up some pastpaper question...may be i cud help u then!!

I hope u can reply asap!! Jazakallah!

i did..u r lucky
Barak Allah feek!

 

[XPFMember]

Re: Maths made easy =) stuck sumwhere?Ask ur doubts here!!

Hey.. there was some formula sheet posted here.. I can't find it now.. can you give me the link please

Assalamoalaikum!!

Here it is

 

[Hassanmahmud]

Re: Maths made easy =) stuck sumwhere?Ask ur doubts here!!

AOA! I couldn't resist solving this
For (a) part, you simply insert the values of x into the respective functions like this:
(i) f(-1/2) = 2(-1/2) - 1 = -1 -1 = -2
(ii) g(-5) = (-5)^2 + 1 = 25 +1 = 26.
(iii) h(-3) = 2^-3 = 1/2^3 = 1/8.

(b) Let y = 2x - 1.
=> x = (y+1)/2
Since f(x) = y, f-1 = x.
f-1 = (y+1)/2.
x and y are just dummy variables so you may write it like this: f-1(x) = (x +1)/2.

(c) g(x) = z.
=> x^2 + 1 = z
=> x^2 = z - 1
=> x = +/- underroot (z - 1).

(d) gf(x) = g(2x - 1) function f is inserted here
= (2x - 1)^2 + 1
= 4x^2 - 4x + 2.

I hope you understand.

Thank you so much

 

[abcde]

Re: Maths made easy =) stuck sumwhere?Ask ur doubts here!!

No problem!

 

[Scarlet]

Re: Maths made easy =) stuck sumwhere?Ask ur doubts here!!

Hey can you help me with Algebra? How do I solve the "express as a single fraction" questions? For example this one :
2X+3 - X+2
4 3

 

[XPFMember]

Re: Maths made easy =) stuck sumwhere?Ask ur doubts here!!

Assalamoalaikum!

find the LCM .. 12..and solve as u do it for normal fractions..
if u have any problem still..let me know! but before i can show u the steps i request u to show me how u wud solve..2/3 + 4/7...bcoz there are diff methods of solving so want to know which method do u follow...

 

[Scarlet]

Re: Maths made easy =) stuck sumwhere?Ask ur doubts here!!

Thank you for replying! And we usually do this usuing calc. but here's how i'd do it :
2/3 + 4/7 (Find LCM, which is 21)
(2x7)/21 + (4x3)/21
14/21 + 12/21 = 26/21

 

[XPFMember]

Re: Maths made easy =) stuck sumwhere?Ask ur doubts here!!

Thank you for replying! And we usually do this usuing calc. but here's how i'd do it :
2/3 + 4/7 (Find LCM, which is 21)
(2x7)/21 + (4x3)/21
14/21 + 12/21 = 26/21

no problem..and thanks for solving..now u have to do the same thing in the other type of question..u can however not solve this by a calculator :!:

Hey can you help me with Algebra? How do I solve the "express as a single fraction" questions? For example this one :
--2X+3 - X+2

• 4 ------ 3

now for this question LCM is 12
so ((2X + 3) x 3)/12 - ((X + 2) x 4 ) / 12 = [(6X + 9) - (4X + 8)] / 12 ...and solve by opening the brackets..

hope this helps

 

[boodi196]

Re: Maths made easy =) stuck sumwhere?Ask ur doubts here!!

Can u help me in physics about KE?
MJ 2009 paper 3 physics question 5 section Bi) PLEASE HELP ME

 

[Smile27]

Re: Maths made easy =) stuck sumwhere?Ask ur doubts here!!

Mathematics IGCSE 0580
October/November Paper 2 -- 2005
Question 7(b)

It's a question about function inverses...

HELP! Please

Thank you.

 

[XPFMember]

Re: Maths made easy =) stuck sumwhere?Ask ur doubts here!!

it'd be better if u cud post the link 2 the paper..it becomes easier 4 me and saves my time

 

[XPFMember]

Re: Maths made easy =) stuck sumwhere?Ask ur doubts here!!

Assalamoalaikum!!

m sorry for the late reply...anyways here u go

whenever u get this type of questions that is u have the eqn of f(x) and u have to find f-1(1) or any other value...u can simply do this by equating the eqn..i mean like f-1(1) means f(x) = 1

so in this case 10^x = 1
and solve this using indices..hope u know that any number to the power of 0 is 1 hence x=0

hope u understood..if u're confused still..let me know..will try to clear urdoubt InshaAllah

Jazak Allah Khair

 

[CaptainDanger]

Re: Maths made easy =) stuck sumwhere?Ask ur doubts here!!

I have a problem sent that to you in a PM???

 

[XPFMember]

Re: Maths made easy =) stuck sumwhere?Ask ur doubts here!!

Assalamoalaikum!!

i have my exams...soon...and atm m doing my homework...u do one thing give me the link to the paper. will try to do it at the earliest inshaAllah!!..

hope u dont mind!

 

[CaptainDanger]

Re: Maths made easy =) stuck sumwhere?Ask ur doubts here!!

Thanks..

Here is the link... Q10 a iii part
http://www.xtremepapers.net/CIE/index.p ... _qp_21.pdf