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Pertanyaan

Diketahui  fungsi begin mathsize 14px style f colon R rightwards arrow R end style dan begin mathsize 14px style g colon R rightwards arrow R end style. Jika diketahui begin mathsize 14px style f open parentheses 2 x plus 1 close parentheses equals 6 x minus 9 end style dan begin mathsize 14px style g open parentheses x minus 2 close parentheses equals x squared plus 4 x end style, Fungsi begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses x close parentheses end style adalah ...  

  1.    begin mathsize 14px style 3 x squared plus 12 x plus 24 end style 

  2. begin mathsize 14px style 3 x squared plus 12 x plus 48 end style  

  3. begin mathsize 14px style 3 x squared plus 24 x plus 12 end style 

  4. begin mathsize 14px style 3 x squared plus 24 x plus 24 end style 

  5. begin mathsize 14px style 3 x squared plus 24 x plus 36 end style 

I. Roy

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D

Pembahasan

Pertama akan dicari fungsi begin mathsize 14px style f open parentheses x close parentheses end style  dengan cara berikut.

begin mathsize 14px style f open parentheses 2 x plus 1 close parentheses equals 6 x minus 9 end style  

misal begin mathsize 14px style a equals 2 x plus 1 left right double arrow x equals fraction numerator a minus 1 over denominator 2 end fraction end style  

begin mathsize 14px style f open parentheses a close parentheses equals 6 open parentheses fraction numerator a minus 1 over denominator 2 end fraction close parentheses minus 9 space space space space space space equals 3 open parentheses a minus 1 close parentheses minus 9 space space space space space space equals 3 a minus 3 minus 9 space space space space space space equals 3 a minus 12 f open parentheses x close parentheses equals 3 x minus 12 end style   

Akan dicari begin mathsize 14px style g open parentheses x close parentheses end style dengan cara berikut

begin mathsize 14px style g open parentheses x minus 2 close parentheses equals x squared plus 4 x end style  

misal begin mathsize 14px style x minus 2 equals a left right double arrow x equals a plus 2 end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell g open parentheses a close parentheses end cell equals cell open parentheses a plus 2 close parentheses squared plus 4 open parentheses a plus 2 close parentheses end cell row cell space space space space space space end cell equals cell a squared plus 4 a plus 4 plus 4 a plus 8 end cell row cell space space space space space space end cell equals cell a squared plus 8 a plus 12 end cell row cell g open parentheses x close parentheses end cell equals cell x squared plus 8 x plus 12 end cell end table end style 

Selanjutnya akan ditentukan  begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses x close parentheses end style 

begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses x close parentheses equals f open parentheses g open parentheses x close parentheses close parentheses space space space space space space space space space space space space space equals f open parentheses x squared plus 8 x plus 12 close parentheses space space space space space space space space space space space space space equals 3 open parentheses x squared plus 8 x plus 12 close parentheses minus 12 space space space space space space space space space space space space space equals 3 x squared plus 24 x plus 36 minus 12 space space space space space space space space space space space space space equals 3 x squared plus 24 x plus 24 end style  

Jadi,jawaban yang tepat adalah D

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