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Pertanyaan

Diberikan begin mathsize 14px style f left parenthesis x right parenthesis equals p x plus q end style dan begin mathsize 14px style left parenthesis f ring operator f ring operator f right parenthesis left parenthesis x right parenthesis equals 8 x minus 21 end style.

Tentukan : b. pernyataan untuk begin mathsize 14px style open parentheses f ring operator f ring operator f ring operator f close parentheses open parentheses x close parentheses end style.

S. Sutisna

Master Teacher

Mahasiswa/Alumni Unindra PGRI

Jawaban terverifikasi

Pembahasan

Sebelumnya akan dicari nilai begin mathsize 14px style p end style dan undefined.

Diberikan begin mathsize 14px style f left parenthesis x right parenthesis equals p x plus q end style dan begin mathsize 14px style left parenthesis f ring operator f ring operator f right parenthesis left parenthesis x right parenthesis equals 8 x minus 21 end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis f ring operator f ring operator f right parenthesis left parenthesis x right parenthesis end cell equals cell f left parenthesis f left parenthesis f left parenthesis x right parenthesis right parenthesis right parenthesis end cell row cell 8 x minus 21 end cell equals cell f left parenthesis f left parenthesis p x plus q right parenthesis right parenthesis end cell row cell 8 x minus 21 end cell equals cell f left parenthesis p left parenthesis p x plus q right parenthesis plus q right parenthesis end cell row cell 8 x minus 21 end cell equals cell p open square brackets p left parenthesis p x plus q right parenthesis plus q close square brackets plus q end cell row cell 8 x minus 21 end cell equals cell p open parentheses p squared x plus p q plus q close parentheses plus q end cell row cell 8 x minus 21 end cell equals cell p cubed x plus open parentheses p squared q plus p q plus q close parentheses end cell end table end style 

Dari persamaan di atas diperoleh

begin mathsize 14px style p cubed equals 8 left right double arrow p equals 2 end style 

dan begin mathsize 14px style p squared q plus p q plus q equals negative 21 end style.

Akan dicari nilai begin mathsize 14px style q end style, dengan mensubstitusikan begin mathsize 14px style p equals 2 end style ke begin mathsize 14px style p squared q plus p q plus q equals negative 21 end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell p squared q plus p q plus q end cell equals cell negative 21 end cell row cell 2 squared q plus 2 times q plus q end cell equals cell negative 21 end cell row cell 4 q plus 2 q plus q end cell equals cell negative 21 end cell row cell 7 q end cell equals cell negative 21 end cell row q equals cell negative 21 over 7 end cell row q equals cell negative 3 end cell row blank blank blank end table end style 

Jadi, diperoleh undefined dan begin mathsize 14px style q equals negative 3 end style.

Sehingga diperoleh begin mathsize 14px style f left parenthesis x right parenthesis equals 2 x minus 3 end style. Selanjutnya

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis f ring operator f ring operator f ring operator f right parenthesis left parenthesis x right parenthesis end cell equals cell f left parenthesis f left parenthesis f left parenthesis f left parenthesis x right parenthesis right parenthesis right parenthesis right parenthesis end cell row blank equals cell f left parenthesis f left parenthesis f left parenthesis 2 x minus 3 right parenthesis right parenthesis right parenthesis end cell row blank equals cell f left parenthesis f left parenthesis 2 left parenthesis 2 x minus 3 right parenthesis minus 3 right parenthesis right parenthesis end cell row blank equals cell f left parenthesis f left parenthesis 4 x minus 9 right parenthesis right parenthesis end cell row blank equals cell f left parenthesis 2 left parenthesis 4 x minus 9 right parenthesis minus 3 right parenthesis end cell row blank equals cell f left parenthesis 8 x minus 21 right parenthesis end cell row blank equals cell 2 left parenthesis 8 x minus 21 right parenthesis minus 3 end cell row blank equals cell 16 x minus 45 end cell end table end style 

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