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Diketahui f(x)=2x−5, g−1(x)=4x+3​ dan h−1(x)=8x+1. Nilai (f∘(g∘h))−1(−7) adalah....

Pertanyaan

Diketahui begin mathsize 14px style f open parentheses x close parentheses equals 2 x minus 5 comma space g to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator x plus 3 over denominator 4 end fraction end style dan begin mathsize 14px style h to the power of negative 1 end exponent open parentheses x close parentheses equals 8 x plus 1 end style. Nilai begin mathsize 14px style open parentheses f ring operator open parentheses g ring operator h close parentheses close parentheses to the power of negative 1 end exponent open parentheses negative 7 close parentheses end style adalah....

E. Nur

Master Teacher

Mahasiswa/Alumni Institut Teknologi Sepuluh Nopember

Jawaban terverifikasi

Jawaban

hasil dari begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis f ring operator left parenthesis g ring operator h right parenthesis right parenthesis to the power of negative 1 end exponent left parenthesis negative 7 right parenthesis end cell equals 5 end table end style.

Pembahasan

Dengan menggunakan konsep invers fungsi komposisi maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f ring operator open parentheses g ring operator h close parentheses close parentheses to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell open parentheses g ring operator h close parentheses to the power of negative 1 end exponent open parentheses x close parentheses ring operator f to the power of negative 1 end exponent open parentheses x close parentheses end cell row blank equals cell h to the power of negative 1 end exponent open parentheses x close parentheses ring operator g to the power of negative 1 end exponent open parentheses x close parentheses ring operator f to the power of negative 1 end exponent open parentheses x close parentheses end cell end table end style

Tentukan dahulu begin mathsize 14px style f to the power of negative 1 end exponent open parentheses x close parentheses end style. Misalkan begin mathsize 14px style f open parentheses x close parentheses equals y end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals y row cell 2 x minus 5 end cell equals y row cell 2 x end cell equals cell y plus 5 end cell row x equals cell fraction numerator y plus 5 over denominator 2 end fraction end cell row cell f to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator x plus 5 over denominator 2 end fraction end cell end table end style

Sehingga didapat

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis f ring operator open parentheses g ring operator h close parentheses right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell h to the power of negative 1 end exponent left parenthesis x right parenthesis ring operator g to the power of negative 1 end exponent left parenthesis x right parenthesis ring operator f to the power of negative 1 end exponent left parenthesis x right parenthesis end cell row blank equals cell h to the power of negative 1 end exponent open parentheses g to the power of negative 1 end exponent open parentheses f to the power of negative 1 end exponent open parentheses x close parentheses close parentheses close parentheses end cell row blank equals cell h to the power of negative 1 end exponent open parentheses left parenthesis g to the power of negative 1 end exponent open parentheses fraction numerator x plus 5 over denominator 2 end fraction close parentheses right parenthesis close parentheses end cell row blank equals cell h to the power of negative 1 end exponent open parentheses left parenthesis fraction numerator fraction numerator x plus 5 over denominator 2 end fraction plus 3 over denominator 4 end fraction right parenthesis close parentheses end cell row blank equals cell h to the power of negative 1 end exponent left parenthesis fraction numerator x plus 11 over denominator 8 end fraction right parenthesis end cell row blank equals cell 8 left parenthesis fraction numerator x plus 11 over denominator 8 end fraction right parenthesis plus 1 end cell row blank equals cell x plus 11 plus 1 end cell row blank equals cell x plus 12 end cell row cell left parenthesis f ring operator left parenthesis g ring operator h right parenthesis right parenthesis to the power of negative 1 end exponent left parenthesis negative 7 right parenthesis end cell equals cell negative 7 plus 12 end cell row blank equals 5 end table end style

Dengan demikian hasil dari begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis f ring operator left parenthesis g ring operator h right parenthesis right parenthesis to the power of negative 1 end exponent left parenthesis negative 7 right parenthesis end cell equals 5 end table end style.

218

4.9 (13 rating)

Titis Widiyawati

Bantu banget

Adelia Putri

Makasih ❤️

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Diketahui fungsi f:R→R, g:R→R, dan h:R→R. Jika fungsi f(x)=4−3x2, g(x)=xx+2​​, dan (f∘g∘h)−1(x)=3x​. Tentukan fungsi h(x).

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