Roboguru
SD
SMP
SMA
UTBK/SNBT

Iklan

Pertanyaan

Misalkan . Nilai maksimum untuk (f(x))² dengan x merupakanbilangan real adalah ....

Misalkan begin mathsize 14px style straight f open parentheses straight x close parentheses equals open parentheses square root of 2 plus 1 close parentheses sin invisible function application straight x plus open parentheses square root of 2 minus 1 close parentheses cos invisible function application straight x end style. Nilai maksimum untuk (f(x))² dengan x merupakan bilangan real adalah ....

  1. –6

  2. –3

  3. 0

  4. 3

  5. 6

Ikuti Tryout SNBT & Menangkan E-Wallet 100rb

Habis dalam

00

:

04

:

35

:

18

Klaim

Iklan

R. Rohmat

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah E.

jawaban yang tepat adalah E.

Pembahasan

Perhatikan bahwa Perhatikan bahwa : dengan Perhatikan bentuk . Karena dan b = 1, maka : Sehingga . Maka Ingat bahwa Sehingga nilai maksimum untuk (f(x))² adalah 6. Jadi, jawaban yang tepat adalah E.

Perhatikan bahwa

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight f open parentheses straight x close parentheses end cell equals cell open parentheses square root of 2 plus 1 close parentheses sin invisible function application straight x plus open parentheses square root of 2 minus 1 close parentheses cos invisible function application straight x end cell row cell open parentheses straight f open parentheses straight x close parentheses close parentheses squared end cell equals cell open parentheses open parentheses square root of 2 plus 1 close parentheses sin invisible function application straight x plus open parentheses square root of 2 minus 1 close parentheses cos invisible function application straight x close parentheses squared end cell row cell open parentheses straight f open parentheses straight x close parentheses close parentheses squared end cell equals cell open parentheses open parentheses square root of 2 plus 1 close parentheses sin invisible function application straight x close parentheses squared plus 2 open parentheses square root of 2 plus 1 close parentheses sin invisible function application straight x open parentheses square root of 2 minus 1 close parentheses cos invisible function application straight x plus open parentheses open parentheses square root of 2 minus 1 close parentheses cos invisible function application straight x close parentheses squared end cell row cell open parentheses straight f open parentheses straight x close parentheses close parentheses squared end cell equals cell open parentheses square root of 2 plus 1 close parentheses squared sin squared invisible function application straight x plus 2 sin invisible function application xcos invisible function application straight x open parentheses square root of 2 plus 1 close parentheses open parentheses square root of 2 minus 1 close parentheses plus open parentheses square root of 2 minus 1 close parentheses squared cos squared invisible function application straight x end cell row cell open parentheses straight f open parentheses straight x close parentheses close parentheses squared end cell equals cell open parentheses square root of 2 plus 1 close parentheses squared sin squared invisible function application straight x plus 2 sin invisible function application xcos invisible function application straight x open parentheses 2 minus 1 close parentheses plus open parentheses square root of 2 minus 1 close parentheses squared cos squared invisible function application straight x end cell row cell open parentheses straight f open parentheses straight x close parentheses close parentheses squared end cell equals cell open parentheses square root of 2 plus 1 close parentheses squared sin squared invisible function application straight x plus 2 sin invisible function application xcos invisible function application straight x open parentheses 1 close parentheses plus open parentheses square root of 2 minus 1 close parentheses squared cos squared invisible function application straight x end cell row cell open parentheses straight f open parentheses straight x close parentheses close parentheses squared end cell equals cell open parentheses square root of 2 plus 1 close parentheses squared sin squared invisible function application straight x plus 2 sin invisible function application xcos invisible function application straight x plus open parentheses square root of 2 minus 1 close parentheses squared cos squared invisible function application straight x end cell row cell open parentheses straight f open parentheses straight x close parentheses close parentheses squared end cell equals cell open parentheses square root of 2 plus 1 close parentheses squared sin squared invisible function application straight x plus sin invisible function application 2 straight x plus open parentheses square root of 2 minus 1 close parentheses squared cos squared invisible function application straight x end cell row cell open parentheses straight f open parentheses straight x close parentheses close parentheses squared end cell equals cell open parentheses square root of 2 plus 1 close parentheses squared sin squared invisible function application straight x plus open parentheses square root of 2 minus 1 close parentheses squared cos squared invisible function application straight x plus sin invisible function application 2 straight x end cell row cell open parentheses straight f open parentheses straight x close parentheses close parentheses squared end cell equals cell open parentheses 2 plus 2 square root of 2 plus 1 close parentheses sin squared invisible function application straight x plus open parentheses 2 minus 2 square root of 2 plus 1 close parentheses cos squared invisible function application straight x plus sin invisible function application 2 straight x end cell row cell open parentheses straight f open parentheses straight x close parentheses close parentheses squared end cell equals cell open parentheses 3 plus 2 square root of 2 close parentheses sin squared invisible function application straight x plus open parentheses 3 minus 2 square root of 2 close parentheses cos squared invisible function application straight x plus sin invisible function application 2 straight x end cell row cell open parentheses straight f open parentheses straight x close parentheses close parentheses squared end cell equals cell 3 sin squared invisible function application straight x plus 2 square root of 2 sin squared invisible function application straight x plus 3 cos squared invisible function application straight x minus 2 square root of 2 cos squared invisible function application straight x plus sin invisible function application 2 straight x end cell row cell open parentheses straight f open parentheses straight x close parentheses close parentheses squared end cell equals cell 3 sin squared invisible function application straight x plus 3 cos squared invisible function application straight x minus 2 square root of 2 cos squared invisible function application straight x plus 2 square root of 2 sin squared invisible function application straight x plus sin invisible function application 2 straight x end cell row cell open parentheses straight f open parentheses straight x close parentheses close parentheses squared end cell equals cell 3 open parentheses sin squared invisible function application straight x plus cos squared invisible function application straight x close parentheses minus 2 square root of 2 open parentheses cos squared invisible function application straight x minus sin squared invisible function application straight x close parentheses plus sin invisible function application 2 straight x end cell row cell open parentheses straight f open parentheses straight x close parentheses close parentheses squared end cell equals cell 3 open parentheses 1 close parentheses minus 2 square root of 2 cos invisible function application 2 straight x plus sin invisible function application 2 straight x end cell row cell open parentheses straight f open parentheses straight x close parentheses close parentheses squared end cell equals cell 3 minus 2 square root of 2 cos invisible function application 2 straight x plus sin invisible function application 2 straight x end cell end table end style 


Perhatikan bahwa :

begin mathsize 14px style straight a space cos invisible function application straight x plus straight b space sin invisible function application straight x equals straight k space cos invisible function application open parentheses straight x minus straight alpha close parentheses end style 

dengan begin mathsize 14px style straight k equals square root of straight a squared plus straight b squared end root end style 


Perhatikan bentuk begin mathsize 14px style negative 2 square root of 2 cos invisible function application 2 straight x plus sin invisible function application 2 straight x end style. Karena begin mathsize 14px style straight a equals negative 2 square root of 2 end style dan b = 1, maka :

 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row straight k equals cell square root of open parentheses negative 2 square root of 2 close parentheses squared plus 1 squared end root end cell row blank equals cell square root of 8 plus 1 end root end cell row blank equals cell square root of 9 end cell row blank equals 3 end table end style 

Sehingga begin mathsize 14px style negative 2 square root of 2 cos invisible function application 2 straight x plus sin invisible function application 2 straight x equals 3 cos invisible function application open parentheses 2 straight x minus straight alpha close parentheses end style.


Maka 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses straight f open parentheses straight x close parentheses close parentheses squared end cell equals cell 3 minus 2 square root of 2 cos invisible function application 2 straight x plus sin invisible function application 2 straight x end cell row cell open parentheses straight f open parentheses straight x close parentheses close parentheses squared end cell equals cell 3 plus 3 cos invisible function application open parentheses 2 straight x minus straight alpha close parentheses end cell end table end style 


Ingat bahwa 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell negative 1 end cell less or equal than cell cos invisible function application straight x less or equal than 1 end cell row cell negative 1 end cell less or equal than cell cos invisible function application open parentheses 2 straight x minus straight alpha close parentheses less or equal than 1 end cell row cell negative 3 end cell less or equal than cell 3 cos invisible function application open parentheses 2 straight x minus straight alpha close parentheses less or equal than 3 end cell row cell 3 minus 3 end cell less or equal than cell 3 plus 3 cos invisible function application open parentheses 2 straight x minus straight alpha close parentheses less or equal than 3 plus 3 end cell row 0 less or equal than cell 3 plus 3 cos invisible function application open parentheses 2 straight x minus straight alpha close parentheses less or equal than 6 end cell row 0 less or equal than cell open parentheses straight f open parentheses straight x close parentheses close parentheses squared less or equal than 6 end cell end table end style 

Sehingga nilai maksimum untuk (f(x))² adalah 6.

Jadi, jawaban yang tepat adalah E.

Perdalam pemahamanmu bersama Master Teacher
di sesi Live Teaching, GRATIS!

1

Iklan

Gold Icon

Klaim Gold gratis sekarang!

Dengan Gold kamu bisa tanya soal ke Forum sepuasnya, lho.

Pertanyaan serupa

Misalkan , maka nilai maksimum dari 2(f(x))² adalah ....

3

0.0

Jawaban terverifikasi

Misalkan , maka nilai maksimum dari 2(f(x))² adalah ....

3

0.0

Jawaban terverifikasi

Iklan

Nilai-nilai x, untuk 0° ≤ x ≤ 360° yang memenuhi sin ⁡x + sin ⁡2x > sin⁡ 3x adalah ....

2

0.0

Jawaban terverifikasi

cos⁡ α ⋅ cos⁡ 2α ⋅ cos ⁡4α ⋅ cos ⁡8α⋅…⋅cos⁡ 2 2020 α = ....

7

0.0

Jawaban terverifikasi

Himpunan semua bilangan real x pada selang ( 0, 2 π) yang memenuhi 2 − 2 sin 2 x ≤ 3 ​ cos x berbentuk .Nilai a + b + c + d adalah ....

14

0.0

Jawaban terverifikasi
Ruangguru

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Roboguru

Download di Google Play

Coba GRATIS Aplikasi Ruangguru

Download di Google PlayDownload di AppstoreDownload di App Gallery

Produk Ruangguru

Produk Lainnya

Bantuan & Panduan

Hubungi Kami

Ruangguru WhatsApp

+62 815-7441-0000

Email info@ruangguru.com

[email protected]

Contact 02140008000

02140008000

Ikuti Kami

©2025 Ruangguru. All Rights Reserved PT. Ruang Raya Indonesia