Pertanyaan

Diketahui dan g(x) = -x + 2, x ∈ R. Jika , maka nilai a adalah ....

A. Rizky

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

jawabannya adalah D.

Pembahasan

Pertama, kita cari masing-masing dan . Sehingga Jadi, jawabannya adalah D.

Pertama, kita cari masing-masing dan .

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell 2 x minus a plus 3 end cell row y equals cell 2 x minus a plus 3 end cell row cell y plus a minus 3 end cell equals cell 2 x end cell row cell fraction numerator y plus a minus 3 over denominator 2 end fraction end cell equals x row blank blank blank row cell f open parentheses x close parentheses end cell equals y row cell f to the power of negative 1 end exponent open parentheses y close parentheses end cell equals x row cell f to the power of negative 1 end exponent open parentheses y close parentheses end cell equals cell fraction numerator y plus a minus 3 over denominator 2 end fraction end cell row cell f to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator x plus a minus 3 over denominator 2 end fraction end cell row blank blank blank row cell g open parentheses x close parentheses end cell equals cell negative x plus 2 end cell row y equals cell negative x plus 2 end cell row cell y minus 2 end cell equals cell negative x end cell row cell 2 minus y end cell equals x row blank blank blank row cell g open parentheses x close parentheses end cell equals y row cell g to the power of negative 1 end exponent open parentheses y close parentheses end cell equals x row cell g to the power of negative 1 end exponent open parentheses y close parentheses end cell equals cell 2 minus y end cell row cell g to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell 2 minus x end cell end table end style$

Sehingga

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

Jadi, jawabannya adalah D.