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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 3 x minus 4 close parentheses equals 5 x minus 1 end style dan begin mathsize 14px style g open parentheses x plus 2 close parentheses equals x squared plus 3 x minus 2 end style. Nilai Fungsi begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses negative 2 close parentheses end style adalah ...  

I. Roy

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

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 3 x minus 4 close parentheses equals 5 x minus 1 end style  

misal begin mathsize 14px style a equals 3 x minus 4 left right double arrow x equals fraction numerator a plus 4 over denominator 3 end fraction end style   

begin mathsize 14px style f open parentheses a close parentheses equals 5 open parentheses fraction numerator a plus 4 over denominator 3 end fraction close parentheses minus 1 f open parentheses a close parentheses equals fraction numerator 5 a plus 20 minus 3 over denominator 3 end fraction f open parentheses a close parentheses equals fraction numerator 5 a plus 17 over denominator 3 end fraction f open parentheses x close parentheses equals fraction numerator 5 x plus 17 over denominator 3 end fraction 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 plus 2 close parentheses equals x squared plus 3 x minus 2 end style  

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

 begin mathsize 14px style g open parentheses a close parentheses equals open parentheses a minus 2 close parentheses squared plus 3 open parentheses a minus 2 close parentheses minus 2 g open parentheses a close parentheses equals a squared minus 4 a plus 4 plus 3 a minus 6 minus 2 g open parentheses a close parentheses equals a squared minus a minus 4 g open parentheses x close parentheses equals x squared minus x minus 4 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 minus x minus 4 close parentheses space space space space space space space space space space space space space equals fraction numerator 5 open parentheses x squared minus x minus 4 close parentheses plus 17 over denominator 3 end fraction space space space space space space space space space space space space space equals fraction numerator 5 x squared minus 5 x minus 20 plus 17 over denominator 3 end fraction space space space space space space space space space space space space space equals fraction numerator 5 x squared minus 5 x minus 3 over denominator 3 end fraction end style    

Nilai Fungsi begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses negative 2 close parentheses end style 

begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses negative 2 close parentheses equals fraction numerator 5 open parentheses negative 2 close parentheses squared minus 5 open parentheses negative 2 close parentheses minus 3 over denominator 3 end fraction space space space space space space space space space space space space space space space space equals fraction numerator 20 plus 10 minus 3 over denominator 3 end fraction space space space space space space space space space space space space space space space space equals 9 space space space space space end style 

Jadi, nilai dari begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses negative 2 close parentheses end style adalah 9

 

 

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