Iklan

Iklan

Pertanyaan

Diketahui fungsi f : R → R dan f ( x ) = x 2 + 2 x − 3 .Jika daerah asal fungsi tersebut adalah D f ​ = { x ∣ − 4 ≤ x ≤ 2 , x ∈ R } . Tentukan daerah hasilnya!

Diketahui fungsi  dan .Jika daerah asal fungsi tersebut adalah . Tentukan daerah hasilnya!

 

Iklan

F. Kurnia

Master Teacher

Mahasiswa/Alumni Universitas Jember

Jawaban terverifikasi

Iklan

Pembahasan

Pada , nilai .adalah ; ; ; ; ; Nilai dari . Jadi batasan nilai atau daerah hasil dari untuk adalah .

Pada  begin mathsize 14px style f left parenthesis x right parenthesis equals x squared plus 2 x minus 3 end style, nilai begin mathsize 14px style f open parentheses negative 4 close parentheses comma space f open parentheses negative 3 close parentheses comma space f open parentheses negative 2 close parentheses comma space f open parentheses negative 1 close parentheses comma space f open parentheses 0 close parentheses comma space dan space f open parentheses 2 close parentheses end style.adalah

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis negative 4 right parenthesis end cell equals cell left parenthesis negative 4 right parenthesis squared plus 2 left parenthesis negative 4 right parenthesis minus 3 end cell row blank equals cell 16 minus 8 minus 3 end cell row blank equals cell 16 minus 11 end cell row blank equals 5 end table end stylebegin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis negative 3 right parenthesis end cell equals cell left parenthesis negative 3 right parenthesis squared plus 2 left parenthesis negative 3 right parenthesis minus 3 end cell row blank equals cell 9 minus 6 minus 3 end cell row blank equals cell 9 minus 9 end cell row blank equals 0 end table end stylebegin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis negative 2 right parenthesis end cell equals cell left parenthesis negative 2 right parenthesis squared plus 2 left parenthesis negative 2 right parenthesis minus 3 end cell row blank equals cell 4 minus 4 minus 3 end cell row blank equals cell 4 minus 7 end cell row blank equals cell negative 3 end cell end table end stylebegin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis negative 1 right parenthesis end cell equals cell left parenthesis negative 1 right parenthesis squared plus 2 left parenthesis negative 1 right parenthesis minus 3 end cell row blank equals cell 1 minus 2 minus 3 end cell row blank equals cell 1 minus 5 end cell row blank equals cell negative 4 end cell end table end stylebegin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis 0 right parenthesis end cell equals cell left parenthesis 0 right parenthesis squared plus 2 left parenthesis 0 right parenthesis minus 3 end cell row blank equals cell 0 plus 0 minus 3 end cell row blank equals cell 0 minus 3 end cell row blank equals cell negative 3 end cell end table end stylebegin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis 2 right parenthesis end cell equals cell left parenthesis 2 right parenthesis squared plus 2 left parenthesis 2 right parenthesis minus 3 end cell row blank equals cell 4 plus 4 minus 3 end cell row blank equals cell 8 minus 3 end cell row blank equals 5 end table end style

Nilai dari begin mathsize 14px style f left parenthesis negative 4 right parenthesis equals 5 comma space f left parenthesis negative 3 right parenthesis equals 0 comma space f left parenthesis negative 2 right parenthesis equals negative 3 comma space f left parenthesis negative 1 right parenthesis equals negative 4 comma space f left parenthesis 0 right parenthesis equals negative 3 comma space dan space f left parenthesis 2 right parenthesis equals 5 end style.

Jadi batasan nilai begin mathsize 14px style y end style atau daerah hasil dari begin mathsize 14px style f left parenthesis x right parenthesis equals x squared plus 2 x minus 3 end style untuk begin mathsize 14px style D subscript f equals left curly bracket x vertical line minus 4 less or equal than x less or equal than 2 comma x element of R right curly bracket end style adalah begin mathsize 14px style R subscript f equals left curly bracket y vertical line minus 4 less or equal than y less or equal than 5 comma y element of R right curly bracket end style.

 

 

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

11

Harly Harly

Pembahasan lengkap banget

Edwin Dwi Saputra Bancin

Jawaban tidak sesuai

Iklan

Iklan

Pertanyaan serupa

Diketahui fungsi linear f ( x ) = 2 x − 4 dengan daerah asal D f ​ = { x ∣ − 3 ≤ x ≤ 5 } . Tentukan R f ​ !

13

4.4

Jawaban terverifikasi

RUANGGURU HQ

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

Coba GRATIS Aplikasi Roboguru

Coba GRATIS Aplikasi Ruangguru

Download di Google PlayDownload di AppstoreDownload di App Gallery

Produk Ruangguru

Hubungi Kami

Ruangguru WhatsApp

+62 815-7441-0000

Email info@ruangguru.com

[email protected]

Contact 02140008000

02140008000

Ikuti Kami

©2024 Ruangguru. All Rights Reserved PT. Ruang Raya Indonesia