Pertanyaan

Diketahui dua fungsi polinomial h(x) adalah g(x). Jika dan maka ….

Diketahui dua fungsi polinomial h(x) adalah g(x). Jika $begin mathsize 14px style fraction numerator h open parentheses x close parentheses over denominator g open parentheses x close parentheses end fraction equals 1 third x comma end style$ dan maka ….

h(x) =
h(x) = 2
h(x) = 3
h(x) = 9
h(x) = 27

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Habis dalam

Klaim

H. Nufus

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Pembahasan

Perhatikan bahwa dari sini diperoleh Selanjutnya, perhatikan bahwa Substitusi x = g(x), diperoleh Jadi, didapat

Perhatikan bahwa

dari sini diperoleh

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator d over denominator d x end fraction open parentheses integral open parentheses h ring operator g close parentheses open parentheses x close parentheses blank d x close parentheses end cell equals cell fraction numerator d over denominator d x end fraction open parentheses 27 over 7 x to the power of 7 plus C close parentheses end cell row cell open parentheses h ring operator g close parentheses open parentheses x close parentheses end cell equals cell 27 over 7 times 7 times x to the power of 6 plus 0 end cell row cell open parentheses h ring operator g close parentheses open parentheses x close parentheses end cell equals cell 27 x to the power of 6 end cell end table end style$

Selanjutnya, perhatikan bahwa

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator h open parentheses x close parentheses over denominator g open parentheses x close parentheses end fraction end cell equals cell 1 third x end cell row cell h open parentheses x close parentheses end cell equals cell 1 third x times g open parentheses x close parentheses end cell end table end style$

Substitusi x = g(x), diperoleh

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell h open parentheses g open parentheses x close parentheses close parentheses end cell equals cell 1 third open parentheses g open parentheses x close parentheses close parentheses times g open parentheses g open parentheses x close parentheses close parentheses end cell row cell open parentheses h ring operator g close parentheses open parentheses x close parentheses end cell equals cell fraction numerator g open parentheses x close parentheses over denominator 3 end fraction times open parentheses g ring operator g close parentheses open parentheses x close parentheses end cell row cell 27 x to the power of 6 end cell equals cell fraction numerator g open parentheses x close parentheses over denominator 3 end fraction times 27 x to the power of 4 end cell row cell fraction numerator 27 x to the power of 6 over denominator 27 x to the power of 4 end fraction end cell equals cell fraction numerator g open parentheses x close parentheses over denominator 3 end fraction end cell row cell x squared end cell equals cell fraction numerator g open parentheses x close parentheses over denominator 3 end fraction end cell row cell 3 x squared end cell equals cell g open parentheses x close parentheses end cell end table end style$

Jadi, didapat

$begin mathsize 14px style fraction numerator h open parentheses x close parentheses over denominator g open parentheses x close parentheses end fraction equals 1 third x fraction numerator h open parentheses x close parentheses over denominator 3 x squared end fraction equals 1 third x h open parentheses x close parentheses equals 1 third x times 3 x squared h open parentheses x close parentheses equals x cubed end style$