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Pertanyaan

Diketahui space fungsi space straight f colon straight R rightwards arrow straight R space dan space straight g colon straight R rightwards arrow straight R space dirumuskan  dengan space straight f left parenthesis straight x right parenthesis equals 2 straight x minus 1 space dan space straight g left parenthesis straight x right parenthesis equals fraction numerator straight x plus 3 over denominator 2 minus straight x end fraction comma straight x not equal to 2.  Fungsi space invers space dari space left parenthesis straight f ring operator straight g right parenthesis left parenthesis straight x right parenthesis space adalah equals....

  1. left parenthesis f o g right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis fraction numerator 2 x plus 4 over denominator x plus 3 end fraction comma x not equal to negative 3

  2. left parenthesis f o g right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis fraction numerator 2 x minus 4 over denominator x plus 3 end fraction comma x not equal to negative 3

  3. left parenthesis f o g right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis fraction numerator 2 x plus 4 over denominator x minus 3 end fraction comma x not equal to 3

  4. left parenthesis f o g right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis fraction numerator 3 x minus 2 over denominator 2 x plus 2 end fraction comma x not equal to negative 1

  5. left parenthesis f o g right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis fraction numerator 3 x minus 2 over denominator negative 2 x plus 2 end fraction comma x not equal to 1

F. Kurnia

Master Teacher

Mahasiswa/Alumni Universitas Jember

Jawaban terverifikasi

Pembahasan

left parenthesis straight f ring operator straight g right parenthesis left parenthesis straight x right parenthesis equals straight f left parenthesis straight g left parenthesis straight x right parenthesis right parenthesis  left parenthesis straight f ring operator straight g right parenthesis left parenthesis straight x right parenthesis equals straight f open parentheses fraction numerator straight x plus 3 over denominator 2 minus straight x end fraction close parentheses  left parenthesis straight f ring operator straight g right parenthesis left parenthesis straight x right parenthesis equals 2 open parentheses fraction numerator straight x plus 3 over denominator 2 minus straight x end fraction close parentheses minus 1  left parenthesis straight f ring operator straight g right parenthesis left parenthesis straight x right parenthesis equals fraction numerator 2 straight x plus 6 over denominator 2 minus straight x end fraction minus 1  left parenthesis straight f ring operator straight g right parenthesis left parenthesis straight x right parenthesis equals fraction numerator 2 straight x plus 6 minus 1 left parenthesis 2 minus straight x right parenthesis over denominator 2 minus straight x end fraction  left parenthesis straight f ring operator straight g right parenthesis left parenthesis straight x right parenthesis equals fraction numerator 3 straight x plus 4 over denominator 2 minus straight x end fraction equals fraction numerator 3 straight x plus 4 over denominator negative straight x plus 2 end fraction    Invers space dari space straight h left parenthesis straight x right parenthesis equals fraction numerator ax plus straight b over denominator cx plus straight d end fraction space adalah space straight h to the power of negative 1 end exponent left parenthesis straight x right parenthesis equals fraction numerator negative dx plus straight b over denominator cx minus straight a end fraction  Sehingga space invers space dari space left parenthesis straight f ring operator straight g right parenthesis left parenthesis straight x right parenthesis equals fraction numerator 3 straight x plus 4 over denominator negative straight x plus 2 end fraction space adalah  left parenthesis straight f ring operator straight g right parenthesis to the power of negative 1 end exponent left parenthesis straight x right parenthesis equals fraction numerator negative 2 straight x plus 4 over denominator negative straight x minus 3 end fraction  left parenthesis straight f ring operator straight g right parenthesis to the power of negative 1 end exponent left parenthesis straight x right parenthesis equals fraction numerator 2 straight x minus 4 over denominator straight x plus 3 end fraction

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