Roboguru

Jika , invers dark fungsi adalah.

Pertanyaan

Jika h left parenthesis x right parenthesis equals x squared plus 10 x plus 15, invers dark fungsi h left parenthesis x right parenthesis adalah.

  1. h to the power of negative 1 end exponent left parenthesis x right parenthesis equals negative 10 plus-or-minus square root of x plus 10 end root comma space x greater or equal than negative 10

  2. h to the power of negative 1 end exponent left parenthesis x right parenthesis equals negative 5 plus-or-minus square root of x minus 10 end root comma space x greater or equal than negative 10

  3. h to the power of negative 1 end exponent left parenthesis x right parenthesis equals negative 5 plus-or-minus square root of x plus 10 end root comma space x greater or equal than negative 10

  4. h to the power of negative 1 end exponent left parenthesis x right parenthesis equals negative 10 plus-or-minus square root of x minus 10 end root comma space x greater or equal than negative 10

Pembahasan Soal:

Untuk menentukan invers dari fungsi kuadrat, kita dapat menggunkan metode kuadran sempurna:

table attributes columnalign right center left columnspacing 0px end attributes row cell h left parenthesis x right parenthesis end cell equals cell x squared plus 10 x plus 15 end cell row y equals cell x squared plus 10 x plus 15 end cell row cell y minus 15 end cell equals cell x squared plus 10 x end cell row cell y minus 15 plus open parentheses 10 over 2 close parentheses squared end cell equals cell x squared plus 10 x plus open parentheses 10 over 2 close parentheses squared end cell row cell y minus 15 plus 25 end cell equals cell left parenthesis x plus 5 right parenthesis squared y plus 10 equals left parenthesis x plus 5 right parenthesis squared end cell row cell left parenthesis x plus 5 right parenthesis squared end cell equals cell y plus 10 end cell row cell x plus 5 end cell equals cell plus-or-minus square root of y plus 10 end root end cell row x equals cell negative 5 plus-or-minus square root of y plus 10 end root end cell row cell h to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell negative 5 plus-or-minus square root of x plus 10 end root comma space x greater or equal than negative 10 end cell end table

Jadi, jawaban yang tepat adalah C

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

M. Nasrullah

Mahasiswa/Alumni Universitas Negeri Makassar

Terakhir diupdate 02 Mei 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

Tapi Roboguru masih mau belajar. Menurut kamu pembahasan kali ini sudah membantu, belum?

Membantu

Kurang Membantu

Apakah pembahasan ini membantu?

Belum menemukan yang kamu cari?

Post pertanyaanmu ke Tanya Jawab, yuk

Mau Bertanya

Pertanyaan yang serupa

Diketahui fungsi  dengan , maka fungsi invers =....

Pembahasan Soal:

Berdasarkan sifat fungsi invers, maka didapatkan :

table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell x squared minus 2 x minus 3 end cell row y equals cell x squared minus 2 x minus 3 end cell row cell y plus 4 end cell equals cell x squared minus 2 x minus 3 plus 4 end cell row cell y plus 4 end cell equals cell x squared minus 2 x plus 1 end cell row cell y plus 4 end cell equals cell open parentheses x minus 1 close parentheses squared end cell row cell x minus 1 end cell equals cell plus-or-minus square root of y plus 4 end root end cell row x equals cell 1 plus-or-minus square root of y plus 4 end root end cell row cell f to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell 1 plus-or-minus square root of x plus 4 end root end cell end table

Maka fungsi invers adalah f to the power of negative 1 end exponent left parenthesis x right parenthesis equals 1 plus-or-minus square root of x plus 4 end root 

Oleh karena itu, jawaban yang benar adalah C

0

Roboguru

Diketahui  dan  maka nilai dari  adalah ....

Pembahasan Soal:

Diberikan fungsi f left parenthesis x right parenthesis equals x minus 6 dan fungsi komposisi open parentheses f ring operator g close parentheses left parenthesis x right parenthesis equals x squared plus 4 x minus 2. Fungsi g left parenthesis x right parenthesis dapat dihitung seperti berikut :

table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis g left parenthesis x right parenthesis right parenthesis end cell equals cell x squared plus 4 x minus 2 end cell row cell g left parenthesis x right parenthesis minus 6 end cell equals cell x squared plus 4 x minus 2 end cell row cell g left parenthesis x right parenthesis end cell equals cell x squared plus 4 x minus 2 plus 6 end cell row cell g left parenthesis x right parenthesis end cell equals cell x squared plus 4 x plus 4 end cell end table 

Dimisalkan fungsi g left parenthesis x right parenthesis equals y maka

table attributes columnalign right center left columnspacing 0px end attributes row y equals cell x squared plus 4 x plus 4 end cell row y equals cell left parenthesis x plus 2 right parenthesis squared end cell row cell square root of y end cell equals cell square root of left parenthesis x plus 2 right parenthesis squared end root end cell row cell square root of y end cell equals cell x plus 2 end cell row x equals cell square root of y minus 2 end cell end table

Jadi, nilai dari g to the power of negative 1 end exponent left parenthesis x right parenthesis adalah g to the power of negative 1 end exponent left parenthesis x right parenthesis equals square root of x minus 2.

0

Roboguru

Diketahui fungsi  dan . Tentukanlah  dan !

Pembahasan Soal:

Dengan menerapkan konsep komposisi fungsi.

left parenthesis straight f ring operator straight g right parenthesis left parenthesis straight x plus 1 right parenthesis equals negative 2 straight x minus 4 straight x – 1 

Misalkan

 p equals x plus 1 x equals p minus 1 

Maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis straight f ring operator straight g right parenthesis left parenthesis straight x plus 1 right parenthesis end cell equals cell negative 2 straight x squared minus 4 straight x – 1 end cell row cell left parenthesis straight f ring operator straight g right parenthesis left parenthesis p right parenthesis end cell equals cell negative 2 left parenthesis p minus 1 right parenthesis squared minus 4 left parenthesis p minus 1 right parenthesis – 1 end cell row blank equals cell negative 2 left parenthesis p squared minus 2 p plus 1 right parenthesis minus 4 p plus 4 minus 1 end cell row blank equals cell negative 2 p squared plus 4 p minus 2 minus 4 p plus 3 end cell row blank equals cell negative 2 p squared plus 1 end cell row cell left parenthesis straight f ring operator straight g right parenthesis left parenthesis x right parenthesis end cell equals cell negative 2 x squared plus 1 end cell end table 

table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis straight f ring operator straight g right parenthesis left parenthesis straight x right parenthesis end cell equals cell negative 2 straight x squared plus 1 end cell row cell straight f left parenthesis straight g left parenthesis straight x right parenthesis right parenthesis end cell equals cell negative 2 straight x squared plus 1 end cell row cell 2 straight g left parenthesis straight x right parenthesis plus 3 end cell equals cell negative 2 straight x squared plus 1 end cell row cell 2 straight g left parenthesis straight x right parenthesis end cell equals cell negative 2 straight x squared minus 2 end cell row cell straight g left parenthesis straight x right parenthesis end cell equals cell fraction numerator negative 2 straight x squared minus 2 over denominator 2 end fraction end cell row cell straight g left parenthesis straight x right parenthesis end cell equals cell negative straight x squared minus 1 end cell end table   

Invers fungsi:

Misalkan g left parenthesis x right parenthesis equals y rightwards arrow x equals g to the power of negative 1 end exponent left parenthesis y right parenthesis 

table attributes columnalign right center left columnspacing 0px end attributes row cell straight g left parenthesis straight x right parenthesis end cell equals cell negative straight x squared minus 1 end cell row straight y equals cell negative straight x squared minus 1 end cell row cell straight y plus 1 end cell equals cell negative straight x blank squared end cell row cell negative left parenthesis straight y plus 1 right parenthesis end cell equals cell straight x blank squared end cell row cell plus-or-minus square root of negative left parenthesis straight y plus 1 right parenthesis end root end cell equals straight x row cell plus-or-minus square root of negative left parenthesis straight y plus 1 right parenthesis end root end cell equals cell straight g to the power of negative 1 end exponent left parenthesis straight y right parenthesis end cell row cell plus-or-minus square root of negative left parenthesis straight x plus 1 right parenthesis end root end cell equals cell straight g to the power of negative 1 end exponent left parenthesis straight x right parenthesis end cell end table  

Maka: 

table attributes columnalign right center left columnspacing 0px end attributes row cell straight g to the power of negative 1 end exponent left parenthesis straight x right parenthesis end cell equals cell plus-or-minus square root of negative left parenthesis straight x plus 1 right parenthesis end root end cell row cell straight g to the power of negative 1 end exponent left parenthesis negative 2 right parenthesis end cell equals cell plus-or-minus square root of negative left parenthesis negative 2 plus 1 right parenthesis end root end cell row blank equals cell square root of negative left parenthesis negative 1 right parenthesis end root end cell row blank equals cell square root of 1 end cell row blank equals 1 end table 

Jadii, table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight g to the power of negative 1 end exponent left parenthesis straight x right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus-or-minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of negative left parenthesis straight x plus 1 right parenthesis end root end cell end table dan table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight g to the power of negative 1 end exponent left parenthesis negative 2 right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table 1

0

Roboguru

Jika , invers dari fungsi tersebut adalah ...

Pembahasan Soal:

Fungsi invers atau fungsi kebalikan merupakan suatu fungsi yang berkebalikan dari fungsi asalnya. 

space space f left parenthesis x right parenthesis space equals space x ² minus space 2 x space plus space 4

table attributes columnalign right center left columnspacing 0px end attributes row cell straight m straight i straight s straight a straight l space y end cell equals cell f open parentheses x close parentheses end cell row blank blank blank row y equals cell x squared minus 2 x plus 4 end cell row cell y minus 4 end cell equals cell x squared minus 2 x end cell row cell y minus 4 plus 1 end cell equals cell x squared minus 2 x plus 1 end cell row cell y minus 3 end cell equals cell open parentheses x minus 1 close parentheses squared end cell row cell square root of y minus 3 end root end cell equals cell x minus 1 end cell row x equals cell square root of y minus 3 end root plus 1 end cell row cell f to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell square root of x minus 3 end root plus 1 end cell end table 

Dengan demikian, fungsi invers dari space space f left parenthesis x right parenthesis space equals space x ² minus space 2 x space plus space 4 adalah table attributes columnalign right center left columnspacing 0px end attributes row cell f to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell square root of x minus 3 end root plus 1 end cell end table.

0

Roboguru

Tentukan fungsi invers dari .

Pembahasan Soal:

Ada 3 langkah untuk menentukan fungsi invers, yaitu:

1. Ubahlah bentuk begin mathsize 14px style y equals f open parentheses x close parentheses end style menjadi bentuk size 14px x size 14px equals size 14px f begin mathsize 14px style left parenthesis y right parenthesis end style.

2. Tuliskan begin mathsize 14px style x end style sebagai begin mathsize 14px style f to the power of negative 1 end exponent open parentheses y close parentheses end style sehingga begin mathsize 14px style f to the power of negative 1 end exponent left parenthesis y right parenthesis equals f left parenthesis y right parenthesis end style.

3. Ubahlah variabel y dengan x sehingga diperoleh rumus fungsi invers begin mathsize 14px style f to the power of negative 1 end exponent open parentheses x close parentheses end style.

Oleh karena itu, misalkan begin mathsize 14px style y equals f open parentheses x close parentheses end style. Maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row y equals cell 3 x squared minus 4 end cell row cell y plus 4 end cell equals cell 3 x squared end cell row cell fraction numerator y plus 4 over denominator 3 end fraction end cell equals cell x squared end cell row cell plus-or-minus square root of fraction numerator y plus 4 over denominator 3 end fraction end root end cell equals x end table end style

Dengan demikian, begin mathsize 14px style italic f to the power of negative sign 1 end exponent left parenthesis italic y right parenthesis equals plus-or-minus square root of fraction numerator italic y plus 4 over denominator 3 end fraction end root end style dan mengakibatkan begin mathsize 14px style f to the power of negative 1 end exponent left parenthesis x right parenthesis equals plus-or-minus square root of fraction numerator x plus 4 over denominator 3 end fraction end root end style, dengan syarat size 14px x size 14px greater or equal than size 14px minus size 14px 4 agar bentuk akarnya terdefinisi.

Jadi, begin mathsize 14px style f to the power of negative 1 end exponent left parenthesis x right parenthesis equals plus-or-minus square root of fraction numerator x plus 4 over denominator 3 end fraction end root comma space x greater or equal than negative 4 end style.

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

Tapi Roboguru masih mau belajar. Menurut kamu pembahasan kali ini sudah membantu, belum?

Membantu

Kurang Membantu

Apakah pembahasan ini membantu?

Belum menemukan yang kamu cari?

Post pertanyaanmu ke Tanya Jawab, yuk

Mau Bertanya

RUANGGURU HQ

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

Coba GRATIS Aplikasi Ruangguru

Produk Ruangguru

Produk Lainnya

Hubungi Kami

Ikuti Kami

©2021 Ruangguru. All Rights Reserved