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Pertanyaan

Jika begin mathsize 14px style f left parenthesis x right parenthesis equals 2 x plus 3 end style dan begin mathsize 14px style g left parenthesis x right parenthesis equals 9 minus x end style, nilai dari begin mathsize 14px style left parenthesis f ring operator g right parenthesis to the power of negative 1 end exponent left parenthesis negative 9 right parenthesis equals end style ....

  1. 32 begin mathsize 14px style space end style 

  2. 16 begin mathsize 14px style space end style 

  3. 15 begin mathsize 14px style space end style 

  4. 13 begin mathsize 14px style space end style 

  5. 22 begin mathsize 14px style space end style 

N. Indah

Master Teacher

Mahasiswa/Alumni Universitas Diponegoro

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C.

Pembahasan

Mencari fungsi f to the power of negative 1 end exponent left parenthesis x right parenthesis 

table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell 2 x plus 3 end cell row y equals cell 2 x plus 3 end cell row cell 2 x end cell equals cell y minus 3 end cell row x equals cell fraction numerator y minus 3 over denominator 2 end fraction end cell end table 

Maka diperoleh f to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator x minus 3 over denominator 2 end fraction.

Mencari fungsi g to the power of negative 1 end exponent left parenthesis x right parenthesis 

table attributes columnalign right center left columnspacing 0px end attributes row cell g left parenthesis x right parenthesis end cell equals cell 9 minus x end cell row y equals cell 9 minus x end cell row x equals cell 9 minus y end cell end table  

Maka diperoleh g to the power of negative 1 end exponent left parenthesis x right parenthesis equals 9 minus x.

Selanjutnya mencari fungsi left parenthesis f ring operator g right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis 

table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis f ring operator g right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell left parenthesis g to the power of negative 1 end exponent ring operator f to the power of negative 1 end exponent right parenthesis left parenthesis x right parenthesis end cell row blank equals cell g to the power of negative 1 end exponent left parenthesis f to the power of negative 1 end exponent left parenthesis x right parenthesis right parenthesis space space end cell row blank equals cell 9 minus open parentheses fraction numerator x minus 3 over denominator 2 end fraction close parentheses end cell end table 

Substitusikan nilai x equals negative 9, sehingga diperoleh left parenthesis f ring operator g right parenthesis to the power of negative 1 end exponent left parenthesis negative 9 right parenthesis adalah:

table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis f ring operator g right parenthesis to the power of negative 1 end exponent left parenthesis negative 9 right parenthesis end cell equals cell 9 minus open parentheses fraction numerator negative 9 minus 3 over denominator 2 end fraction close parentheses end cell row blank equals cell 9 minus open parentheses fraction numerator negative 12 over denominator 2 end fraction close parentheses end cell row blank equals cell 9 minus left parenthesis negative 6 right parenthesis end cell row blank equals cell 9 plus 6 end cell row blank equals 15 end table 

Oleh karena itu, jawaban yang benar adalah C.

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