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Pertanyaan

Fungsi invers dari begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator c minus d x over denominator b x minus a end fraction comma space x not equal to a over b end style adalah ....

  1. begin mathsize 14px style f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator c x minus a over denominator d x minus b x end fraction end style 

  2. begin mathsize 14px style f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator a x minus c over denominator b x minus d end fraction end style 

  3. begin mathsize 14px style f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator c x plus a over denominator d x plus b end fraction end style 

  4. begin mathsize 14px style f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator c x plus a over denominator b x plus d end fraction end style 

  5. begin mathsize 14px style f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator a x plus c over denominator b x plus d end fraction end style 

I. Roy

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Pembahasan

Dapat diperiksa bahwa fungsi begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator c minus d x over denominator b x minus a end fraction comma space x not equal to a over b end style bersifat bijektif sehingga berlaku f(x) = y. Kemudian, perhatikan bahwa

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 cell fraction numerator c minus d x over denominator b x minus a end fraction end cell row y equals cell fraction numerator c minus d x over denominator b x minus a end fraction end cell row cell y open parentheses b x minus a close parentheses end cell equals cell c minus d x end cell row cell b x y minus a y end cell equals cell c minus d x end cell row cell b x y plus d x end cell equals cell a y plus c end cell row cell x open parentheses b y plus d close parentheses end cell equals cell a y plus c end cell row x equals cell fraction numerator a y plus c over denominator b y plus d end fraction end cell end table end style

Kemudian, dengan menggunakan konsep invers kita punya undefined sehingga

begin mathsize 14px style f to the power of negative 1 end exponent open parentheses y close parentheses equals x f to the power of negative 1 end exponent open parentheses y close parentheses equals fraction numerator a y plus c over denominator b y plus d end fraction f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator a x plus c over denominator b x plus d end fraction end style

Jadi, jawaban yang tepat adalah E.

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