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Diketahui f ( x ) = 2 x + 4 , g ( x ) = x 2 − 2 x + 3 , dan . Jika , maka penjumlahan semua nilai x yang mungkin adalah ....

Diketahui , dan begin mathsize 14px style straight h open parentheses straight x close parentheses equals 2 minus straight x end style. Jika begin mathsize 14px style open parentheses straight f ring operator straight g ring operator straight h close parentheses open parentheses straight x close parentheses equals open parentheses straight h ring operator straight g ring operator straight f close parentheses open parentheses straight x close parentheses end style, maka penjumlahan semua nilai x yang mungkin adalah ....

  1. begin mathsize 14px style 4 over 3 end style 

  2. begin mathsize 14px style negative 4 over 3 end style 

  3. undefined 

  4. begin mathsize 14px style negative 19 over 6 end style 

  5. begin mathsize 14px style 19 over 6 end style 

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Perhatikan bahwa bentuk merupakan persamaan kuadrat yang memiliki dua penyelesaian. Misalkan dua penyelesaian tersebut adalah dan , maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses straight f ring operator straight g ring operator straight h close parentheses open parentheses straight x close parentheses end cell equals cell open parentheses straight h ring operator straight g ring operator straight f close parentheses open parentheses straight x close parentheses end cell row cell straight f open parentheses straight g open parentheses straight h open parentheses straight x close parentheses close parentheses close parentheses end cell equals cell straight h open parentheses straight g open parentheses straight f open parentheses straight x close parentheses close parentheses close parentheses end cell row cell straight f open parentheses straight g open parentheses 2 minus straight x close parentheses close parentheses end cell equals cell straight h open parentheses straight g open parentheses 2 straight x plus 4 close parentheses close parentheses end cell row cell straight f open parentheses open parentheses 2 minus straight x close parentheses squared minus 2 open parentheses 2 minus straight x close parentheses plus 3 close parentheses end cell equals cell straight h open parentheses open parentheses 2 straight x plus 4 close parentheses squared minus 2 open parentheses 2 straight x plus 4 close parentheses plus 3 close parentheses end cell row cell straight f open parentheses 4 minus 4 straight x plus straight x squared minus 4 plus 2 straight x plus 3 close parentheses end cell equals cell straight h open parentheses 4 straight x squared plus 16 straight x plus 16 minus 4 straight x minus 8 plus 3 close parentheses end cell row cell straight f open parentheses straight x squared minus 2 straight x plus 3 close parentheses end cell equals cell straight h open parentheses 4 straight x squared plus 12 straight x plus 11 close parentheses end cell row cell 2 open parentheses straight x squared minus 2 straight x plus 3 close parentheses plus 4 end cell equals cell 2 minus open parentheses 4 straight x squared plus 12 straight x plus 11 close parentheses end cell row cell 2 straight x squared minus 4 straight x plus 6 plus 4 end cell equals cell 2 minus 4 straight x squared minus 12 straight x minus 11 end cell row cell 2 straight x squared minus 4 straight x plus 10 end cell equals cell negative 4 straight x squared minus 12 straight x minus 9 end cell row cell 2 straight x squared plus 4 straight x squared minus 4 straight x plus 12 straight x plus 10 plus 9 end cell equals 0 row cell 6 straight x squared plus 8 straight x plus 19 end cell equals 0 end table end style 

Perhatikan bahwa bentuk begin mathsize 14px style 6 straight x squared plus 8 straight x plus 19 equals 0 end style merupakan persamaan kuadrat yang memiliki dua penyelesaian. Misalkan dua penyelesaian tersebut adalah begin mathsize 14px style straight x subscript 1 end style dan begin mathsize 14px style straight x subscript 2 end style, maka

begin mathsize 14px style straight x subscript 1 plus straight x subscript 2 equals negative 8 over 6 equals negative 4 over 3 end style 

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