Jika f(x−5)=xx+2​ maka f−1(x)= ...

Pertanyaan

Jika f open parentheses x minus 5 close parentheses equals fraction numerator x plus 2 over denominator x end fraction maka f to the power of negative 1 end exponent open parentheses x close parentheses equals ...

  1. fraction numerator x plus 7 over denominator x plus 5 end fraction

  2. fraction numerator x minus 3 over denominator x minus 5 end fraction

  3. fraction numerator negative 5 x plus 7 over denominator x minus 1 end fraction

  4. fraction numerator 5 x minus 3 over denominator x minus 1 end fraction

  5. fraction numerator 2 over denominator x minus 1 end fraction

S. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. DR. Hamka

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

Diketahui:

Fungsi f open parentheses x minus 5 close parentheses equals fraction numerator x plus 2 over denominator x end fraction.

Tentukan terlebih dahulu fungsi f open parentheses x close parentheses.

Misal:

table attributes columnalign right center left columnspacing 0px end attributes row cell x minus 5 end cell equals a row x equals cell a plus 5 end cell end table

Maka,

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x minus 5 close parentheses end cell equals cell fraction numerator x plus 2 over denominator x end fraction end cell row cell f open parentheses a close parentheses end cell equals cell fraction numerator a plus 5 plus 2 over denominator a plus 5 end fraction end cell row blank equals cell fraction numerator a plus 7 over denominator a plus 5 end fraction end cell row cell f open parentheses x close parentheses end cell equals cell fraction numerator x plus 7 over denominator x plus 5 end fraction end cell end table

Kemudian cari nilai invers dari fungsi rasionalnya.

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell fraction numerator x plus 7 over denominator x plus 5 end fraction end cell row y equals cell fraction numerator x plus 7 over denominator x plus 5 end fraction end cell row cell y open parentheses x plus 5 close parentheses end cell equals cell x plus 7 end cell row cell x y plus 5 y end cell equals cell x plus 7 end cell row cell x y minus x end cell equals cell negative 5 y plus 7 end cell row cell x open parentheses y minus 1 close parentheses end cell equals cell negative 5 y plus 7 end cell row x equals cell fraction numerator negative 5 y plus 7 over denominator y minus 1 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 negative 5 x plus 7 over denominator x minus 1 end fraction end cell end table

 Maka f to the power of negative 1 end exponent open parentheses x close parentheses equalsfraction numerator negative 5 x plus 7 over denominator x minus 1 end fraction.

Jadi, jawaban yang tepat adalah C.

99

4.5 (9 rating)

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