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Diketahui , , dan . Nilai

Diketahui begin mathsize 14px style f left parenthesis x right parenthesis equals x plus 3 end stylebegin mathsize 14px style g left parenthesis x right parenthesis equals x squared plus 2 x minus 5 end style, dan begin mathsize 14px style h left parenthesis x right parenthesis equals 1 minus 3 x end style. Nilai begin mathsize 14px style open parentheses g ring operator h ring operator f close parentheses left parenthesis negative 2 right parenthesis equals horizontal ellipsis end style 

  1. begin mathsize 14px style 8 end style 

  2.  begin mathsize 14px style 7 end style 

  3. size 14px 3 

  4. size 14px minus size 14px 5 

  5. size 14px minus size 14px 2

Jawaban:

Diketahui fungsi begin mathsize 14px style f left parenthesis x right parenthesis equals x plus 3 end stylebegin mathsize 14px style g left parenthesis x right parenthesis equals x squared plus 2 x minus 5 end style, dan begin mathsize 14px style h left parenthesis x right parenthesis equals 1 minus 3 x end style.

Terlebih dahulu dicari fungsi komposisi begin mathsize 14px style open parentheses h ring operator f close parentheses left parenthesis x right parenthesis end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses h ring operator f close parentheses left parenthesis x right parenthesis end cell equals cell h left parenthesis f left parenthesis x right parenthesis right parenthesis end cell row blank equals cell h left parenthesis x plus 3 right parenthesis end cell row blank equals cell 1 minus 3 left parenthesis x plus 3 right parenthesis end cell row blank equals cell 1 minus 3 x minus 9 end cell row blank equals cell negative 8 minus 3 x end cell end table end style 

Selanjutnya, substitusikan variabel size 14px x dalam begin mathsize 14px style left parenthesis g right parenthesis end style size 14px left parenthesis size 14px x size 14px right parenthesis dengan fungsi komposisi begin mathsize 14px style open parentheses h ring operator f close parentheses left parenthesis x right parenthesis end style seperti berikut,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses g ring operator h ring operator f close parentheses left parenthesis x right parenthesis end cell equals cell g left parenthesis h left parenthesis f left parenthesis x right parenthesis right parenthesis right parenthesis end cell row blank equals cell g left parenthesis negative 8 minus 3 x right parenthesis end cell row blank equals cell left parenthesis negative 8 minus 3 x right parenthesis squared plus 2 left parenthesis negative 8 minus 3 x right parenthesis minus 5 end cell row blank equals cell 64 plus 48 x plus 9 x squared minus 16 minus 6 x minus 5 end cell row blank equals cell 9 x squared plus 42 x plus 43 end cell end table end style 

Untuk mendapatkan nilai fungsi, substitusikan size 14px x size 14px equals size 14px minus size 14px 2 ke dalam fungsi komposisi begin mathsize 14px style open parentheses g ring operator h ring operator f close parentheses left parenthesis x right parenthesis end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses g ring operator h ring operator f close parentheses left parenthesis x right parenthesis end cell equals cell 9 x squared plus 42 x plus 43 end cell row cell open parentheses g ring operator h ring operator f close parentheses left parenthesis negative 2 right parenthesis end cell equals cell 9 left parenthesis negative 2 right parenthesis blank squared plus 42 left parenthesis negative 2 right parenthesis plus 43 end cell row blank equals cell 36 minus 84 plus 43 end cell row blank equals cell negative 5 end cell end table end style 

Dengan demikian, nilai begin mathsize 14px style left parenthesis g ring operator h ring operator f right parenthesis left parenthesis negative 2 right parenthesis end style adalah size 14px minus size 14px 5.

Jadi, jawaban yang tepat adalah D.

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