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!

 

F. Kurnia

Master Teacher

Mahasiswa/Alumni Universitas Jember

Jawaban terverifikasi

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.

 

 

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

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