Math problem

[Queen]

Hi, can u please help me to solve this problem. it's gonna be extra 10 points in test....
f(x)=(x-13)^2/16 this is the given function. Find the three points where this function and its inverse meets/intersects.

[Aman]

If you need help then you need to be more precise about your function. Did you mean
(x-13)^(2/16) or ((x-13)^2)/16

[Aman]

There is no solution, I think. The above mentioned thing is obviously a parabola. It's inverse is
log(x)=((log(16y)*log(13))/2

They simply can't intersect at three points, it is impossible

I maybe wrong though, I am an economist, not mathematician

[Masud]

The only answer I have got so far is:

assuming the given function is (x-13)^2/16

inverse function is y=(16x)^(1/2)+13

the only point these meet is (37.492423,37.492423)

hope this helped a little.

AT

[Queen]

The only answer I have got so far is:

assuming the given function is (x-13)^2/16

inverse function is y=(16x)^(1/2)+13

the only point these meet is (37.492423,37.492423)

hope this helped a little.

AT
Heave, how u calculated this point? u see, square root of 16x, is gonna give two formulas for inverse functions. y=+4x^1/2+13 and y=-4x^1/2+13, which one did u use?

[Queen]

There is no solution, I think. The above mentioned thing is obviously a parabola. It's inverse is
log(x)=((log(16y)*log(13))/2

They simply can't intersect at three points, it is impossible

I maybe wrong though, I am an economist, not mathematician
thank you for trying. I don't think that its inverse includes logs, its iverse should be square root function.

[Mahmud]

1.f(x)=(x-13)^2/16

berilgan funsiyani ikkala qismini 8-darajaga oshiramiz,

[f(x)]^8=x-13

x=[f(x)]^8+13

demakki, teskari funksiya

[f(x)]^-1=x^8+13

{[f(x)]^-1 ni f(x) ga teskari funksiyasi ko'rinishida yozasiz :) }

2.f(x)=[f(x)]^-1 ni tenglashtirib qo'yidagi tenglikka ega bo'lamiz

(x-13)^2/16= x^8+13

bu tenglamani Matlab orqali echasiz :)



Platon.

[Queen]

1.f(x)=(x-13)^2/16

berilgan funsiyani ikkala qismini 8-darajaga oshiramiz,

[f(x)]^8=x-13

x=[f(x)]^8+13

demakki, teskari funksiya

[f(x)]^-1=x^8+13

{[f(x)]^-1 ni f(x) ga teskari funksiyasi ko'rinishida yozasiz :) }

2.f(x)=[f(x)]^-1 ni tenglashtirib qo'yidagi tenglikka ega bo'lamiz

(x-13)^2/16= x^8+13

bu tenglamani Matlab orqali echasiz :)



Platon.
Mahmud batafsil tushuntirib yozganiz uchun rahmat. Lekin bu oddiy precalculusdan misol edi. Matlablani hali oz tarkibiga olmaydi.

[erkak#1]

1.f(x)=(x-13)^2/16

berilgan funsiyani ikkala qismini 8-darajaga oshiramiz,

[f(x)]^8=x-13

x=[f(x)]^8+13

demakki, teskari funksiya

[f(x)]^-1=x^8+13

{[f(x)]^-1 ni f(x) ga teskari funksiyasi ko'rinishida yozasiz :) }

2.f(x)=[f(x)]^-1 ni tenglashtirib qo'yidagi tenglikka ega bo'lamiz

(x-13)^2/16= x^8+13

bu tenglamani Matlab orqali echasiz :)



Platon.
Pythagor janoblari, axiri Platongayam Matlabni o'rgatibsizde a? :lool:

[Aus]

1.f(x)=(x-13)^2/16

berilgan funsiyani ikkala qismini 8-darajaga oshiramiz,

[f(x)]^8=x-13

x=[f(x)]^8+13

demakki, teskari funksiya

[f(x)]^-1=x^8+13

{[f(x)]^-1 ni f(x) ga teskari funksiyasi ko'rinishida yozasiz :) }

2.f(x)=[f(x)]^-1 ni tenglashtirib qo'yidagi tenglikka ega bo'lamiz

(x-13)^2/16= x^8+13

bu tenglamani Matlab orqali echasiz :)



Platon.


heh Norqulakani uquvchilariga uyatamasmi matlab deish a:rolleyes: :rolleyes:

[erkak#1]

heh Norqulakani uquvchilariga uyatamasmi matlab deish a:rolleyes: :rolleyes:
Etgancha Mahmud okamiz Norqulakani qo'lida o'qigandilar-a! :)
Uyat sizga Platon! :lool: :lool:

Aus xonim, UZMU digan thread bolarmidi? :)

[Aus]

Etgancha Mahmud okamiz Norqulakani qo'lida o'qigandilar-a! :)
Uyat sizga Platon! :lool: :lool:

Aus xonim, UZMU digan thread bolarmidi? :)

shu ochvorin uzis kaytatdan UZMU digan thread

Mahmud anaka kalkulatorlani yeg'volardila Norqulaka maktabda Unida esa umuman hayolga keltirish mumkinms edi ...uyat uyat:rolleyes:

[Queen]

heh Norqulakani uquvchilariga uyatamasmi matlab deish a:rolleyes: :rolleyes:
Aus , 243 dagi va UZMUdagi matem oqituvchisi Norqulakani etvossizmi? agar bitta odamni gapirvotgan bolsak, mani ham ustozim bolganlar :)

[Mahmud]

Tabiiy bo'limlar boardida post qilyabsizlar? :)

Joe_Blacke sizam hech shu odatingizni tashlamadingizda :D
Aus masala beruvchi Queen uchun masalani shu qismigacha yozish
yetarli bo'ldi :) {siz masalani qolgan qismini yozishingiz, ya'ni javobni qoldirishingiz mumkin ;) }

Fleym yoki Tanishlarni qidirish boardida thread ochsangizlar yaxshi
bo'lardi :) Man ham shu bahona offtop qilib olardim :shock:

on:yangi masala post qilinibdimi deb o'ylabman :)
yaxshimas.......

[Queen]

Mahmud, threadni ochgan odam offtop qilishga ruhsat bera oladi shekilli. Oshanga ruhsat, offtop qilavering :) agar matematikaga aloqasi bolsa, masaln matematika oqituvchisi haqida.
masalga kesak, thread ochiq, hech kim javob topib bermayotibdi. Dushanba kuni javobini olarman oqishda...
Tabiiy bo'limlar boardida post qilyabsizlar? :)

Joe_Blacke sizam hech shu odatingizni tashlamadingizda :D
Aus masala beruvchi Queen uchun masalani shu qismigacha yozish
yetarli bo'ldi :) {siz masalani qolgan qismini yozishingiz, ya'ni javobni qoldirishingiz mumkin ;) }

Fleym yoki Tanishlarni qidirish boardida thread ochsangizlar yaxshi
bo'lardi :) Man ham shu bahona offtop qilib olardim :shock:

on:yangi masala post qilinibdimi deb o'ylabman :)
yaxshimas.......

[Aus]

Aus , 243 dagi va UZMUdagi matem oqituvchisi Norqulakani etvossizmi? agar bitta odamni gapirvotgan bolsak, mani ham ustozim bolganlar :)


Huddi usha Norqulaka
243 danmisiz??? {Erkinaka boridila yana}

[Queen]

Huddi usha Norqulaka
243 danmisiz??? {Erkinaka boridila yana}
ha 243da oqiganman man ham. Norqulaka bilan Erkinaka 243ning eng kuchli domlalari bolsihgan bolsalar kerak . siz qachon bitirgansiz, 243da oqiganmisiz?

[Aus]

ha 243da oqiganman man ham. Norqulaka bilan Erkinaka 243ning eng kuchli domlalari bolsihgan bolsalar kerak . siz qachon bitirgansiz, 243da oqiganmisiz?


Ugu Norqulakani qullarida uqiganman.....
243 da 11a da edim :)
Fizikadan ABroraka kirarmidila?

[Masud]

Heave, how u calculated this point? u see, square root of 16x, is gonna give two formulas for inverse functions. y=+4x^1/2+13 and y=-4x^1/2+13, which one did u use?

Hello, maybe this opportunity has passed, but still I had to follow up.

In this lazy American High school system or in whatever education step you are on, you have to go by the answers of TI-83 or whichever graphing calculators answers. When you graph square root equation you don't disregard the neagative x-axis. Therefore, there is no side for -4x^(1/2)+13. And when you type in -4x^(1/2)+13 don't forget the (). Or else calculator will assume it is 4x^1 divided by 2.

Hope this helped a little.

AT

[Queen]

Hello, maybe this opportunity has passed, but still I had to follow up.

In this lazy American High school system or in whatever education step you are on, you have to go by the answers of TI-83 or whichever graphing calculators answers. When you graph square root equation you don't disregard the neagative x-axis. Therefore, there is no side for -4x^(1/2)+13. And when you type in -4x^(1/2)+13 don't forget the (). Or else calculator will assume it is 4x^1 divided by 2.

Hope this helped a little.

AT
so u just gave this "magic" TI-83 answers :) ? there should be reason for ignoring -4x... if u come up with solving without calculator, let me know. as teacher still waiting for us to do ourselves.

[Masud]

ok, tried 3 times to write that whole equation. vanished thanks to this forum features.

first of all, if there is no negative side because it is assumed so, when solving equations. you don't just take -4 and 4 out of the square root, you just leave it there as (16)^(1/2)

try to solve degree 4 equation in Precalculus without a graphing calculator.

I am done in this thread, if you want further inquiries, please use PM function.

cheers,
AT

[Queen]

ok, tried 3 times to write that whole equation. vanished thanks to this forum features.

first of all, if there is no negative side because it is assumed so, when solving equations. you don't just take -4 and 4 out of the square root, you just leave it there as (16)^(1/2)

try to solve degree 4 equation in Precalculus without a graphing calculator.

I am done in this thread, if you want further inquiries, please use PM function.

cheers,
AT
it still does not make sense to me why we should not take the square root of 16?! but, that's o.k, I'll just wait for professor's answer. degree 4 equation is just not part of Precalculus, I can't even substitute it with y and solve. there is just different way of solving it. thank you anyways.

[erkak#1]

Qani, hoo Matematiklar! :lool:
Matematikani to'xtatib qo'yish yaxshimas! :lool:

Qani Mahmud oka, bir ikkita Matematik savolladan tashavoring! :lool:
Siz tashamasez Pythagor masala berishga majbur bo'ladi! :lool:

[Pythagor]

315456987841256 songacha bo'lgan tub sonlar sonini toping!

[erkak#1]

315456987841256 songacha bo'lgan tub sonlar sonini toping!
Buni topish uchun matlabni ishlatamiz shakilli :lool:
Osonroq savol yo'qmidi? :lool:

Mayli! Matlab qanisan yordaming kerak! Ooo Matlab.... :lool:

[Afandi007]

Buni topish uchun matlabni ishlatamiz shakilli :lool:
Osonroq savol yo'qmidi? :lool:

Mayli! Matlab qanisan yordaming kerak! Ooo Matlab.... :lool:

Matlab opa shunchala kuchlimi matematikada?

O'zi etishadi ayolla matemda zo'r deb. Maktabdayam Feruzahon bolardi bizda paqat 5 olardi

[Mahmud]

Qani, hoo Matematiklar! :lool:
Matematikani to'xtatib qo'yish yaxshimas! :lool:

Qani Mahmud oka, bir ikkita Matematik savolladan tashavoring! :lool:
Siz tashamasez Pythagor masala berishga majbur bo'ladi! :lool:

Erkak, 10-sinfda ishlagan misollardan bir-ikkitasi esga tushgan misollar;)

http://img97.imageshack.us/img97/9735/13hc.png (http://imageshack.us/?x=my6&myref=http://imageshack.us/)

ps:3-misol Sh.Alimovni 9-sinf kitobida bor:)

[MasxaraboZ]

Matlab opa shunchala kuchlimi matematikada?

O'zi etishadi ayolla matemda zo'r deb. Maktabdayam Feruzahon bolardi bizda paqat 5 olardi

Ayollar Adabiyotda zo'r buladi desangiz tugriroq buladi...undayam faqat she'r ,gazal yozishda...

Kuramiz Afandi007 sizni gapiz qanchalik tugriligini, Mahmud bekni misollariga birinchi bulib qizlar javob berishsa gapimni qaytib olaman...

[MasxaraboZ]

http://img97.imageshack.us/img97/9735/13hc.png (http://imageshack.us/?x=my6&myref=http://imageshack.us/)

1. ikkita tenglamani alohida,alohida yechish kerakmi birgalikdami?
2. a va b sonlarga shart yukmi?

[Mahmud]

1. ikkita tenglamani alohida,alohida yechish kerakmi birgalikdami?
2. a va b sonlarga shart yukmi?

1. Alohida, alohida yechish kerak
2. a soni 0 dan farqli albatta:)

ps: Gentelman misollar juda oddiy bo'lib qolmadimikan?:rolleyes:

[MasxaraboZ]

1. Alohida, alohida yechish kerak
2. a soni 0 dan farqli albatta:)

ps: Gentelman misollar juda oddiy bo'lib qolmadimikan?:rolleyes:





Tushunmadingiz, 2. misolda ixtiyoriy (albatta a noldan farliligi tushunarli) a,b sonlar uchun tengsizlikni sibotlash talab qilinayabdimi? yoki a,b sonlar musbatmi? degan manoda suradim :)

[Mahmud]

Tushunmadingiz, 2. misolda ixtiyoriy (albatta a noldan farliligi tushunarli) a,b sonlar uchun tengsizlikni sibotlash talab qilinayabdimi? yoki a,b sonlar musbatmi? degan manoda suradim :)

Misolni berilishidan yuqorida siz aytib o'tganingizdek ixtiyoriy a,b haqiqiy sonlar uchun tengsizlikni isbotlash kerakligini anglash zarur bo'lardi.Shuning uchun buni yozmay qoldirgandim.

[MasxaraboZ]

...
O'zi etishadi ayolla matemda zo'r deb. Maktabdayam Feruzahon bolardi bizda paqat 5 olardi

Afandi bu ayollar ishonchingizni oqlamadiku, javob berishmayabdiku Mahmudbekni misollariga, yana 5 soat muhlat,javob berishmasa uzim javob beraman:)

[saturn]

sekin-sekin javob berishga harakat qilaman....:)...

xullas, 1- masala:
http://img111.imageshack.us/img111/2372/1masala8dh.jpg

[Mahmud]

sekin-sekin javob berishga harakat qilaman....:)...

xullas, 1- masala:
http://img111.imageshack.us/img111/2372/1masala8dh.jpg

x=1 tenglamani qanoatlantiradi :)

Lekin tenglamada boshqa ildizlar ham bor.
Demak, javobingiz noto'g'ri ;)

[saturn]

ikkinchi ildizi 0.
bu ildiz ildiz ostida qavs ichidagi kavadrat ifodadan kelib chiqadi... (pastdan ikkinchi qatorda)
yani

x + sqrt(sqr(x-1)) = 1 tenglamani x = 1 va x = 0 ga teng bo'gan ikki ildizi bor....
uzr.. bul ifodani qo'shish yodimdan ko'tarulg'on erkan....;)

endi to'g'rimi? yoki yana orqaga qaytib boshqattan echimi?

[MasxaraboZ]

1. Tenglamani yechimlari cheksiz kup va ular [1/2,1] oraliqdagi barcha sonlar.

bu faqat javobi yechilish yuliga keyin tuxtalamiz...Mahmud qaravoring javobim tugrimi ishqilib :)

[Mahmud]

ikkinchi ildizi 0.
bu ildiz ildiz ostida qavs ichidagi kavadrat ifodadan kelib chiqadi... (pastdan ikkinchi qatorda)
yani

x + sqrt(sqr(x-1)) = 1 tenglamani x = 1 va x = 0 ga teng bo'gan ikki ildizi bor....
uzr.. bul ifodani qo'shish yodimdan ko'tarulg'on erkan....;)

endi to'g'rimi? yoki yana orqaga qaytib boshqattan echimi?

qaytadan o'rinib ko'ring...

1. Tenglamani yechimlari cheksiz kup va ular [1/2,1] oraliqdagi barcha sonlar.

bu faqat javobi yechilish yuliga keyin tuxtalamiz...Mahmud qaravoring javobim tugrimi ishqilib :)

javob to'g'ri...

[Bekzod_usa]

Mana birinchisini to'liq yechimi :

Bilmadim to'g'ri bo'lishi kerak...

http://img102.imageshack.us/img102/7678/bekzod023ky.jpg (http://imageshack.us)

[Bekzod_usa]

Shunday qilib javoblarini yozishga joy yetmay qolgandi javoblari:

x 1 dan katta yoki tengligida, tenglama yechimi x=1

x 1 dan kichik bulganda yechim manfiy cheksizlikdan 1 gacha ochiq qavis !

[MasxaraboZ]

Shunday qilib javoblarini yozishga joy yetmay qolgandi javoblari:

x 1 dan katta yoki tengligida, tenglama yechimi x=1

x 1 dan kichik bulganda yechim manfiy cheksizlikdan 1 gacha ochiq qavis !

F(x)= (2x-1)^(1/2) funsiyani aniqlanish sohasini topmabsizu :lool:

shuni topganizda javob tayyor edi :lool:

[Bekzod_usa]

F(x)= (2x-1)^(1/2) funsiyani aniqlanish sohasini topmabsizu :lool:

shuni topganizda javob tayyor edi :lool:

Iye bilmadim lekin javob tashlashimdan oldin, sizni aniqlanish sohani topib bergan javobizni kurib bo'lgandim qaytarib yozib utirgim kelmadi bir hil narsani:lol:

[MasxaraboZ]

Iye bilmadim lekin javob tashlashimdan oldin, sizni aniqlanish sohani topib bergan javobizni kurib bo'lgandim qaytarib yozib utirgim kelmadi bir hil narsani:lol:

qiyinmasu qogozingizni bir joyiga 2x-1 katta yoki teng 0 deb tengsizlikni yechib quysangiz bular ediku :)

mayli keyingi misolga uting Cosx larga :)

[Bekzod_usa]

qiyinmasu qogozingizni bir joyiga 2x-1 katta yoki teng 0 deb tengsizlikni yechib quysangiz bular ediku :)

mayli keyingi misolga uting Cosx larga :)
cosx larniga urinib ko'rdilarmi o'zlari???:lol:

[MasxaraboZ]

cosx larniga urinib ko'rdilarmi o'zlari???:lol:

ha albatta, usha Maxmud bek post qilgan kuni urunib ,ertasiga xal qilgandim :lool:
javobini aytishim mumkin x=Pi/2 + Pi*k , k-ixtiyoriy butun son :)

[Bekzod_usa]

ha albatta, usha Maxmud bek post qilgan kuni urunib ,ertasiga xal qilgandim :lool:
javobini aytishim mumkin x=Pi/2 + Pi*k , k-ixtiyoriy butun son :)
ha gap yo'q lekin mundoq bizga ham yo'l bering urinib ko'raylik hech bo'lmaganda :lol: Endi boshlaymiz-da biz :D

[MasxaraboZ]

ha gap yo'q lekin mundoq bizga ham yo'l bering urinib ko'raylik hech bo'lmaganda :lol: Endi boshlaymiz-da biz :D

Siz bemalol masalalarni yechavering, Mahmudbekdan yangi masalalar kutaib qolamiz :)

[Mahmud]

Tenglamani quyidagicha yechish ham mumkin...

http://img49.imageshack.us/img49/5985/fsf4ks.png (http://imageshack.us/?x=my6&myref=http://www.imageshack.us/)

[MasxaraboZ]

1. Misoldagi cos li tenglama javobi:
Mahmud yechilishida xatoliklar bulsa aytarsiz ,Latex da avval yozib kurmaganman :)

Mahmud siz ham bergan misollarizni attach qilib quysangiz,chunki vaqt utishi bilan linklar eskirsa,sizni quygan suratlar kurinmay qoladi :)

[MasxaraboZ]

2. Tengsizlikni isboti:


Mahmud 3 misolning javobini uzingiz yozing,ancha mehnat talab ekan :lool: