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Diketahui f(x)=2x−3 dan (f∘g)(x)=4x−9. Jika g−1(x) adalah invers dari g(x) maka nilai dari g−1(3)=...

Pertanyaan

Diketahui f left parenthesis x right parenthesis equals 2 x minus 3 dan open parentheses f ring operator g close parentheses left parenthesis x right parenthesis equals 4 x minus 9. Jika g to the power of negative 1 end exponent left parenthesis x right parenthesis adalah invers dari g left parenthesis x right parenthesis maka nilai dari g to the power of negative 1 end exponent left parenthesis 3 right parenthesis equals... 

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I. Sutiawan

Master Teacher

Mahasiswa/Alumni Universitas Pasundan

Jawaban terverifikasi

Jawaban

jawaban yang tepat adaah B

Pembahasan

Diketahui f left parenthesis x right parenthesis equals 2 x minus 3 dan open parentheses f ring operator g close parentheses left parenthesis x right parenthesis equals 4 x minus 9.  Maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f ring operator g close parentheses left parenthesis x right parenthesis end cell equals cell f left parenthesis g left parenthesis x right parenthesis right parenthesis end cell row cell 4 x minus 9 end cell equals cell 2 g left parenthesis x right parenthesis minus 3 end cell row cell 2 g left parenthesis x right parenthesis end cell equals cell 4 x minus 9 plus 3 end cell row cell 2 g left parenthesis x right parenthesis end cell equals cell 4 x minus 6 end cell row cell g left parenthesis x right parenthesis end cell equals cell fraction numerator 4 x minus 6 over denominator 2 end fraction end cell row cell g left parenthesis x right parenthesis end cell equals cell 2 x minus 3 end cell end table

Sehingga: 

table attributes columnalign right center left columnspacing 0px end attributes row cell g left parenthesis x right parenthesis end cell equals cell 2 x minus 3 end cell row y equals cell 2 x minus 3 end cell row cell 2 x end cell equals cell y plus 3 end cell row x equals cell fraction numerator y plus 3 over denominator 2 end fraction end cell row cell g to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell fraction numerator x plus 3 over denominator 2 end fraction end cell row cell g to the power of negative 1 end exponent left parenthesis 3 right parenthesis end cell equals cell fraction numerator 3 plus 3 over denominator 2 end fraction end cell row blank equals cell 6 over 2 end cell row blank equals 3 end table

Jadi, jawaban yang tepat adaah B

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