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Jika rumus f(x)=x+1, g(x)=3x−2, dan h(x)=x2−2x+5 maka nilai (g∘h∘f)(−1) adalah ...

Pertanyaan

Jika rumus f left parenthesis x right parenthesis equals x plus 1g left parenthesis x right parenthesis equals 3 x minus 2, dan h left parenthesis x right parenthesis equals x squared minus 2 x plus 5 maka nilai left parenthesis g ring operator h ring operator f right parenthesis left parenthesis negative 1 right parenthesis adalah ...

  1. negative 7 

  2. negative 2 

  3. 5 

  4. 9 

  5. 13 

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah E.space 

Pembahasan

Diketahui : f left parenthesis x right parenthesis equals x plus 1g left parenthesis x right parenthesis equals 3 x minus 2h left parenthesis x right parenthesis equals x squared minus 2 x plus 5 

Kita cari fungsi left parenthesis h ring operator f right parenthesis left parenthesis x right parenthesis terlebih dahulu

table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis h ring operator f right parenthesis left parenthesis x right parenthesis end cell equals cell h left parenthesis f left parenthesis x right parenthesis right parenthesis end cell row blank equals cell h left parenthesis x plus 1 right parenthesis end cell row blank equals cell left parenthesis x plus 1 right parenthesis squared minus 2 left parenthesis x plus 1 right parenthesis plus 5 end cell row blank equals cell x squared plus 2 x plus 1 minus 2 x minus 2 plus 5 end cell row blank equals cell x squared plus 4 end cell end table 

Selanjutnya mencari fungsi left parenthesis g ring operator h ring operator f right parenthesis left parenthesis x right parenthesis 

table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis g ring operator h ring operator f right parenthesis left parenthesis x right parenthesis end cell equals cell g left parenthesis h left parenthesis f left parenthesis x right parenthesis right parenthesis right parenthesis end cell row blank equals cell g left parenthesis x squared plus 4 right parenthesis end cell row blank equals cell 3 left parenthesis x squared plus 4 right parenthesis minus 2 end cell row blank equals cell 3 x squared plus 12 minus 2 end cell row blank equals cell 3 x squared plus 10 end cell end table 

Lalu substitusikan nilai negative 1 ke fungsi tersebut

table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis g ring operator h ring operator f right parenthesis left parenthesis x right parenthesis end cell equals cell 3 x squared plus 10 end cell row cell left parenthesis g ring operator h ring operator f right parenthesis left parenthesis negative 1 right parenthesis end cell equals cell 3 left parenthesis negative 1 right parenthesis squared plus 10 space end cell row blank equals cell 3 cross times 1 plus 10 end cell row blank equals cell 3 plus 10 end cell row blank equals 13 end table 

 Oleh karena itu, jawaban yang benar adalah E.space 

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