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

Diketahui  dan .

Tentukan:

i.  

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W. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sriwijaya

Jawaban terverifikasi

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hasil dari adalah .

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.

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Pembahasan

Diketahui dan . Maka: Jadi, hasil dari adalah .

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.

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