Diketahui f(x)=2x−1 dan g(x)=x2−3x−6. Tentukan: i. (fg​)(31​)

Pertanyaan

Diketahui begin mathsize 14px style f open parentheses x close parentheses equals 2 x minus 1 end style dan begin mathsize 14px style g open parentheses x close parentheses equals x squared minus 3 x minus 6 end style.

Tentukan:

i. begin mathsize 14px style open parentheses g over f close parentheses open parentheses 1 third close parentheses end style 

W. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sriwijaya

Jawaban terverifikasi

Jawaban

hasil dari begin mathsize 14px style open parentheses g over f close parentheses open parentheses 1 third close parentheses end style adalah begin mathsize 14px style 62 over 3 end style.

Pembahasan

Diketahui begin mathsize 14px style f open parentheses x close parentheses equals 2 x minus 1 end style dan begin mathsize 14px style g open parentheses x close parentheses equals x squared minus 3 x minus 6 end style. Maka:

begin mathsize 14px style space open parentheses g over f close parentheses open parentheses x close parentheses equals fraction numerator x squared minus 3 x minus 6 over denominator 2 x minus 1 end fraction open parentheses g over f close parentheses open parentheses 1 third close parentheses equals fraction numerator open parentheses begin display style 1 third end style close parentheses squared minus 3 open parentheses begin display style 1 third end style close parentheses minus 6 over denominator 2 open parentheses begin display style 1 third end style close parentheses minus 1 end fraction open parentheses g over f close parentheses open parentheses 1 third close parentheses equals fraction numerator 1 over 9 minus 1 minus 6 over denominator 2 over 3 minus 1 end fraction open parentheses g over f close parentheses open parentheses 1 third close parentheses equals fraction numerator begin display style fraction numerator 1 minus 9 minus 54 over denominator 9 end fraction end style over denominator begin display style fraction numerator 2 minus 3 over denominator 3 end fraction end style end fraction open parentheses g over f close parentheses open parentheses 1 third close parentheses equals fraction numerator begin display style fraction numerator negative 62 over denominator 9 end fraction end style over denominator begin display style fraction numerator negative 1 over denominator 3 end fraction end style end fraction open parentheses g over f close parentheses open parentheses 1 third close parentheses equals fraction numerator negative 62 over denominator 9 end fraction cross times fraction numerator 3 over denominator negative 1 end fraction open parentheses g over f close parentheses open parentheses 1 third close parentheses equals fraction numerator negative 186 over denominator negative 9 end fraction open parentheses g over f close parentheses open parentheses 1 third close parentheses equals 62 over 3 end style 

Jadi, hasil dari begin mathsize 14px style open parentheses g over f close parentheses open parentheses 1 third close parentheses end style adalah begin mathsize 14px style 62 over 3 end style.

25

5.0 (3 rating)

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Diketahui f(x+5)=3x2+10x−3 dan g(4x−1)=2x+21−8x​. Tentukan hasil berikut d. (f3g​)(x)

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