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Tentukan fungsi (f+g)(x), (g−f)(x), (f⋅g)(x) dan (gf​)(x) dari fungsi-fungsi berikut: a. f(x)=1+x1−x​ dan g(x)=x1−x​

Pertanyaan

Tentukan fungsi open parentheses f plus g close parentheses open parentheses x close parenthesesopen parentheses g minus f close parentheses open parentheses x close parenthesesopen parentheses f times g close parentheses open parentheses x close parentheses dan open parentheses f over g close parentheses open parentheses x close parentheses dari fungsi-fungsi berikut:

a. f open parentheses x close parentheses equals fraction numerator 1 minus x over denominator 1 plus x end fraction dan g open parentheses x close parentheses equals fraction numerator 1 minus x over denominator x end fraction

Pembahasan Video:

Pembahasan:

  • Hasil operasi fungsi open parentheses f plus g close parentheses open parentheses x close parentheses, yaitu:

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 minus x over denominator 1 plus x end fraction plus fraction numerator 1 minus x over denominator x end fraction end cell row blank equals cell fraction numerator open parentheses 1 minus x close parentheses x over denominator open parentheses 1 plus x close parentheses x end fraction plus fraction numerator open parentheses 1 minus x close parentheses open parentheses 1 plus x close parentheses over denominator x open parentheses 1 plus x close parentheses end fraction end cell row blank equals cell fraction numerator x minus x squared over denominator x plus x squared end fraction plus fraction numerator 1 minus x squared over denominator x plus x squared end fraction end cell row blank equals cell fraction numerator negative 2 x squared plus x plus 1 over denominator x plus x squared end fraction end cell end table

Maka, hasil dari open parentheses f plus g close parentheses open parentheses x close parentheses adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator negative 2 x squared plus x plus 1 over denominator x plus x squared end fraction end cell end table.

 

  • Hasil operasi fungsi open parentheses g minus f close parentheses open parentheses x close parentheses, yaitu:

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

Maka, hasil dari open parentheses g minus f close parentheses open parentheses x close parentheses adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 1 minus x over denominator x plus x squared end fraction end cell end table.

 

  • Hasil operasi fungsi open parentheses f times g close parentheses open parentheses x close parentheses, yaitu:

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

Maka, hasil dari open parentheses f times g close parentheses open parentheses x close parentheses adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 1 minus 2 x plus x squared over denominator x plus x squared end fraction end cell end table.

 

  • Hasil operasi fungsi open parentheses f over g close parentheses open parentheses x close parentheses, yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f over g close parentheses open parentheses x close parentheses end cell equals cell fraction numerator f open parentheses x close parentheses over denominator g open parentheses x close parentheses end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 1 minus x over denominator 1 plus x end fraction end style over denominator begin display style fraction numerator 1 minus x over denominator x end fraction end style end fraction end cell row blank equals cell fraction numerator down diagonal strike 1 minus x end strike over denominator 1 plus x end fraction times fraction numerator x over denominator down diagonal strike 1 minus x end strike end fraction end cell row blank equals cell fraction numerator x over denominator 1 plus x end fraction end cell end table

Maka, hasil dari open parentheses f over g close parentheses open parentheses x close parentheses adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator x over denominator 1 plus x end fraction end cell end table.

Jawaban terverifikasi

Dijawab oleh:

N. Puspita

Terakhir diupdate 07 Oktober 2021

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Tentukan fungsi (f+g)(x), (g−f)(x), (f⋅g)(x) dan (gf​)(x) dari fungsi-fungsi berikut: b. f(x)=x+1​ dan g(x)=x−1​

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