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DIketahui ,  dan . Fungsi komposisi  =....

Pertanyaan

DIketahui f left parenthesis x right parenthesis equals x plus 2, g left parenthesis x right parenthesis equals x squared minus 1 dan h left parenthesis x right parenthesis equals fraction numerator 1 over denominator x plus 1 end fraction. Fungsi komposisi left parenthesis h ring operator g ring operator f right parenthesis left parenthesis x right parenthesis =....

  1. fraction numerator 1 over denominator x squared plus 4 x minus 3 end fraction

  2. fraction numerator 1 over denominator x squared minus 4 x minus 2 end fraction

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

  4. fraction numerator 1 over denominator x squared plus 4 x plus 4 end fraction

  5. fraction numerator 1 over denominator x squared plus 4 x plus 1 end fraction

Pembahasan Soal:

Berdasarkan sifat komposisi fungsi, maka didapatkan :

table attributes columnalign right center left columnspacing 0px end attributes row cell h left parenthesis x right parenthesis end cell equals cell open parentheses fraction numerator 1 over denominator x plus 1 end fraction close parentheses end cell row cell open parentheses h ring operator g close parentheses left parenthesis x right parenthesis end cell equals cell open parentheses fraction numerator 1 over denominator left parenthesis x squared minus 1 right parenthesis plus 1 end fraction close parentheses end cell row blank equals cell open parentheses 1 over x squared close parentheses end cell row cell open parentheses h ring operator g ring operator f close parentheses left parenthesis x right parenthesis end cell equals cell open parentheses 1 over left parenthesis x plus 2 right parenthesis squared close parentheses end cell row blank equals cell fraction numerator 1 over denominator x squared plus 4 x plus 4 end fraction end cell end table

Maka :

table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis f ring operator g ring operator h right parenthesis left parenthesis a right parenthesis end cell equals 11 row cell 4 a squared plus 30 a plus 61 end cell equals 11 row cell 4 a squared plus 30 a plus 61 minus 11 end cell equals 0 row cell 4 a squared plus 30 a plus 50 end cell equals 0 row cell 2 a squared plus 15 a plus 25 end cell equals 0 row cell left parenthesis 2 a plus 5 right parenthesis left parenthesis a plus 5 right parenthesis end cell equals 0 end table

Maka fungsi komposisi left parenthesis h ring operator g ring operator f right parenthesis left parenthesis x right parenthesis adalah fraction numerator 1 over denominator x squared plus 4 x plus 4 end fraction

Oleh karena itu, jawaban yang benar adalah D

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 06 Mei 2021

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