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Jika diketahui  dan . Nilai dari  adalah ....

Pertanyaan

Jika diketahui begin mathsize 14px style f open parentheses x close parentheses equals 12 x squared minus 7 end style dan begin mathsize 14px style g open parentheses 1 over x close parentheses equals fraction numerator x minus 2 over denominator 4 x plus 1 end fraction end style. Nilai dari begin mathsize 14px style f ring operator g open parentheses 2 close parentheses end style adalah ....

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M. Alfi

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

Pembahasan

 Gunakan invers untuk mencari begin mathsize 14px style g left parenthesis x right parenthesis end style:

begin mathsize 14px style u equals 1 over x x equals 1 over u end style  

begin mathsize 14px style g open parentheses u close parentheses equals fraction numerator 1 over u minus 2 over denominator 4 left parenthesis 1 over u right parenthesis plus 1 end fraction g open parentheses u close parentheses equals fraction numerator 1 over u minus fraction numerator 2 u over denominator u end fraction over denominator 4 over u plus 1 end fraction g open parentheses u close parentheses equals fraction numerator 1 over u minus fraction numerator 2 u over denominator u end fraction over denominator 4 over u plus u over u end fraction g open parentheses u close parentheses equals fraction numerator fraction numerator 1 minus 2 u over denominator u end fraction over denominator fraction numerator 4 plus u over denominator u end fraction end fraction g open parentheses u close parentheses equals fraction numerator 1 minus 2 u over denominator 4 plus u end fraction g open parentheses x close parentheses equals fraction numerator 1 minus 2 x over denominator 4 plus x end fraction     end style  

begin mathsize 14px style f ring operator g open parentheses x close parentheses end style adalah fungsi g dimasukkan ke fungsi f

 begin mathsize 14px style g open parentheses 2 close parentheses equals fraction numerator 1 minus 2 left parenthesis 2 right parenthesis over denominator 4 plus 2 end fraction g open parentheses 2 close parentheses equals fraction numerator 1 minus 4 over denominator 6 end fraction g open parentheses 2 close parentheses equals fraction numerator negative 3 over denominator 6 end fraction g open parentheses 2 close parentheses equals negative 1 half end style  

begin mathsize 14px style f ring operator g open parentheses 2 close parentheses equals f open parentheses g open parentheses 2 close parentheses close parentheses equals 12 open parentheses negative 1 half close parentheses squared minus 7 f open parentheses g open parentheses 2 close parentheses close parentheses equals 12 open parentheses 1 fourth close parentheses minus 7 f open parentheses g open parentheses 2 close parentheses close parentheses equals 3 minus 7 f open parentheses g open parentheses 2 close parentheses close parentheses equals negative 4  end style 

Jadi, nilai dari begin mathsize 14px style f ring operator g open parentheses 2 close parentheses end style adalah size 14px minus size 14px 4  

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