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Pertanyaan

a. Jika begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator 2 x plus 1 over denominator x minus 3 end fraction comma blank x not equal to 3 end style dan begin mathsize 14px style g open parentheses x close parentheses equals fraction numerator 4 minus 2 x over denominator x plus 2 end fraction comma blank x not equal to negative 2 end style, tentukan begin mathsize 14px style left parenthesis f blank ring operator blank g right parenthesis left parenthesis x right parenthesis end style.

S. Amamah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

hasil dari  begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses x close parentheses end style  adalah begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 3 x minus 10 over denominator 5 x plus 2 end fraction end cell end table. end style 

Pembahasan

Ingat kembali komposisi dua fungsi:

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 f left parenthesis g open parentheses x close parentheses right parenthesis end cell end table 

sehingga:

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 f left parenthesis g open parentheses x close parentheses right parenthesis end cell row blank equals cell f open parentheses fraction numerator 4 minus 2 x over denominator x plus 2 end fraction close parentheses end cell row blank equals cell fraction numerator 2 begin display style open parentheses fraction numerator 4 minus 2 x over denominator x plus 2 end fraction close parentheses end style plus 1 over denominator begin display style fraction numerator 4 minus 2 x over denominator x plus 2 end fraction minus 3 end style end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 2 open parentheses 4 minus 2 x close parentheses plus open parentheses x plus 2 close parentheses over denominator x plus 2 end fraction end style over denominator begin display style fraction numerator open parentheses 4 minus 2 x close parentheses minus 3 open parentheses x plus 2 close parentheses over denominator x plus 2 end fraction end style end fraction end cell row blank equals cell fraction numerator 8 minus 4 x plus x plus 2 over denominator 4 minus 2 x minus 3 x minus 6 end fraction end cell row blank equals cell fraction numerator negative 3 x plus 10 over denominator negative 5 x minus 2 end fraction end cell row blank equals cell fraction numerator up diagonal strike negative 1 end strike left parenthesis 3 x minus 10 right parenthesis over denominator up diagonal strike negative 1 end strike left parenthesis 5 x plus 2 right parenthesis end fraction end cell row cell left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis end cell equals cell fraction numerator 3 x minus 10 over denominator 5 x plus 2 end fraction end cell end table 

Dengan demikian, hasil dari  begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses x close parentheses end style  adalah begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 3 x minus 10 over denominator 5 x plus 2 end fraction end cell end table. end style 

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