Tentukan rumus g(x) dari tiap kondisi yang diberikan c.      f(x)=x2−2x+2 dan (f∘g)(x)=8x2−16x+15

Pertanyaan

Tentukan rumus begin mathsize 14px style g open parentheses x close parentheses end style dari tiap kondisi yang diberikan

c.      begin mathsize 14px style f open parentheses x close parentheses equals x squared minus 2 x plus 2 end style dan begin mathsize 14px style left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis equals 8 x squared minus 16 x plus 15 end style  

F. Nur

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank g end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis 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 cell fraction numerator 22 plus-or-minus square root of 484 over denominator 16 end fraction end cell end table end style  

Pembahasan

Diketahui begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses x close parentheses end style dan begin mathsize 14px style f open parentheses x close parentheses end style, sehingga

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis end cell equals cell 8 x squared minus 16 x plus 15 end cell row cell f left parenthesis g left parenthesis x right parenthesis right parenthesis end cell equals cell 8 x squared minus 16 x plus 15 end cell row cell g left parenthesis x right parenthesis squared minus 2 g left parenthesis x right parenthesis plus 2 end cell equals cell 8 x squared minus 16 x plus 15 end cell row cell left parenthesis g left parenthesis x right parenthesis squared minus 2 g left parenthesis x right parenthesis plus 1 right parenthesis plus 1 end cell equals cell 8 x squared minus 16 x plus 15 end cell row cell left parenthesis g left parenthesis x right parenthesis minus 1 right parenthesis squared plus 1 end cell equals cell 8 x squared minus 16 x plus 15 end cell row cell square root of left parenthesis g left parenthesis x right parenthesis minus 1 right parenthesis squared end root end cell equals cell square root of 8 x squared minus 16 x plus 14 end root end cell row cell g left parenthesis x right parenthesis minus 1 end cell equals cell fraction numerator 6 plus-or-minus square root of 484 over denominator 16 end fraction end cell row cell g open parentheses x close parentheses end cell equals cell fraction numerator 6 plus-or-minus square root of 484 over denominator 16 end fraction plus 1 end cell row cell g left parenthesis x right parenthesis end cell equals cell fraction numerator 6 plus-or-minus square root of 484 over denominator 16 end fraction plus 16 over 16 end cell row cell g left parenthesis x right parenthesis end cell equals cell fraction numerator 22 plus-or-minus square root of 484 over denominator 16 end fraction end cell end table end style  

Jadi, begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank g end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis 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 cell fraction numerator 22 plus-or-minus square root of 484 over denominator 16 end fraction end cell end table end style  

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