Diketahui fungsi sebagai berikut: f(x)h(x)g(x)m(x)​====​2x+1x−4x2−3x+22x−5x+4​​  Tentukan: d. (m∘f)(x)

Pertanyaan

Diketahui fungsi sebagai berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell f open parentheses x close parentheses end cell equals cell 2 x plus 1 end cell row cell h open parentheses x close parentheses end cell equals cell x minus 4 end cell row cell g open parentheses x close parentheses end cell equals cell x squared minus 3 x plus 2 end cell row cell m open parentheses x close parentheses end cell equals cell fraction numerator x plus 4 over denominator 2 x minus 5 end fraction end cell end table end style 

Tentukan:

d. begin mathsize 14px style open parentheses m ring operator f close parentheses open parentheses x close parentheses end style

Y. Fathoni

Master Teacher

Mahasiswa/Alumni Universitas Negeri Yogyakarta.

Jawaban terverifikasi

Jawaban

diperoleh begin mathsize 14px style open parentheses m ring operator f close parentheses open parentheses x close parentheses equals fraction numerator 2 x plus 5 over denominator 4 x minus 3 end fraction end style.

Pembahasan

Gunakan konsep komposisi fungsi.

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 end style  

Diketahui:

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell f open parentheses x close parentheses end cell equals cell 2 x plus 1 end cell row cell h open parentheses x close parentheses end cell equals cell x minus 4 end cell row cell g open parentheses x close parentheses end cell equals cell x squared minus 3 x plus 2 end cell row cell m open parentheses x close parentheses end cell equals cell fraction numerator x plus 4 over denominator 2 x minus 5 end fraction end cell end table end style

Akan ditentukan begin mathsize 14px style open parentheses m ring operator f close parentheses open parentheses x close parentheses end style, perhatikan perhitungan berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell open parentheses m ring operator f close parentheses open parentheses x close parentheses end cell equals cell m open parentheses f open parentheses x close parentheses close parentheses end cell row blank equals cell m open parentheses 2 x plus 1 close parentheses end cell row blank equals cell fraction numerator open parentheses 2 x plus 1 close parentheses plus 4 over denominator 2 open parentheses 2 x plus 1 close parentheses minus 5 end fraction end cell row blank equals cell fraction numerator 2 x plus 5 over denominator 4 x plus 2 minus 5 end fraction end cell row cell open parentheses m ring operator f close parentheses open parentheses x close parentheses end cell equals cell fraction numerator 2 x plus 5 over denominator 4 x minus 3 end fraction end cell end table end style 

Jadi, diperoleh begin mathsize 14px style open parentheses m ring operator f close parentheses open parentheses x close parentheses equals fraction numerator 2 x plus 5 over denominator 4 x minus 3 end fraction end style.

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