Diketahui f(x)=x+11​ dan g(x)=2x+1x​. Tentukan rumus tiap fungsi yang dinyatakan berikut. (f+g)(x)

Pertanyaan

Diketahui f open parentheses x close parentheses equals fraction numerator 1 over denominator x plus 1 end fraction dan g open parentheses x close parentheses equals fraction numerator x over denominator 2 x plus 1 end fraction. Tentukan rumus tiap fungsi yang dinyatakan berikut.

open parentheses f plus g close parentheses open parentheses x close parentheses

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

open parentheses f plus g close parentheses open parentheses x close parentheses equals fraction numerator x squared plus 3 x plus 1 over denominator open parentheses x plus 1 close parentheses open parentheses 2 x plus 1 close parentheses end fraction atau table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator x squared plus 3 x plus 1 over denominator 2 x squared plus 3 x plus 1 end fraction end cell end table.

Pembahasan

Penjumlahan fungsi f dan g ditulis f plus g didefinisikan sebagai open parentheses f plus g close parentheses open parentheses x close parentheses equals f open parentheses x close parentheses plus g open parentheses x close parentheses.

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f plus g close parentheses open parentheses x close parentheses end cell equals cell f open parentheses x close parentheses plus g open parentheses x close parentheses end cell row blank equals cell fraction numerator 1 over denominator x plus 1 end fraction plus fraction numerator x over denominator 2 x plus 1 end fraction end cell row blank equals cell fraction numerator 2 x plus 1 plus x open parentheses x plus 1 close parentheses over denominator open parentheses x plus 1 close parentheses open parentheses 2 x plus 1 close parentheses end fraction end cell row blank equals cell fraction numerator 2 x plus 1 plus x squared plus x over denominator open parentheses x plus 1 close parentheses open parentheses 2 x plus 1 close parentheses end fraction end cell row blank equals cell fraction numerator x squared plus 3 x plus 1 over denominator open parentheses x plus 1 close parentheses open parentheses 2 x plus 1 close parentheses end fraction end cell row blank equals cell fraction numerator x squared plus 3 x plus 1 over denominator 2 x squared plus 3 x plus 1 end fraction end cell end table

Jadi, open parentheses f plus g close parentheses open parentheses x close parentheses equals fraction numerator x squared plus 3 x plus 1 over denominator open parentheses x plus 1 close parentheses open parentheses 2 x plus 1 close parentheses end fraction atau table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator x squared plus 3 x plus 1 over denominator 2 x squared plus 3 x plus 1 end fraction end cell end table.

38

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Diketahui fungsi polinomial f(x)=x4−2x2−3, g(x)=2x2+4, dan h(x)=6x+4. Jika fungsi q(x)=h(x)⋅f(x)+g(x), tentukan nilai dari: q(−1)?

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