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Diketahui fungsi f(x)=x+12x​, g(x)=4xx−1​, dan h(x)=2x+1​. Tentukan nilai setiap fungsi berikut ini serta daerah asalnya (domain). c. (f−g)(x)

Pertanyaan

Diketahui fungsi f open parentheses x close parentheses equals fraction numerator 2 x over denominator x plus 1 end fractiong open parentheses x close parentheses equals fraction numerator x minus 1 over denominator 4 x end fraction, dan h open parentheses x close parentheses equals fraction numerator x plus 1 over denominator 2 end fraction. Tentukan nilai setiap fungsi berikut ini serta daerah asalnya (domain).

c. open parentheses f minus g close parentheses open parentheses x close parentheses 

N. Puspita

Master Teacher

Jawaban terverifikasi

Pembahasan

Pengurangan kedua fungsi f(x) dan g(x) adalah sebagai berikut:

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f minus g close parentheses open parentheses x close parentheses end cell equals cell fraction numerator 2 x over denominator x plus 1 end fraction minus fraction numerator x minus 1 over denominator 4 x end fraction end cell row blank equals cell fraction numerator open parentheses 2 x close parentheses open parentheses 4 x close parentheses minus open parentheses x minus 1 close parentheses open parentheses x plus 1 close parentheses over denominator open parentheses x plus 1 close parentheses open parentheses 4 x close parentheses end fraction end cell row blank equals cell fraction numerator 8 x squared minus open parentheses x squared minus 1 close parentheses over denominator open parentheses x plus 1 close parentheses open parentheses 4 x close parentheses end fraction end cell row blank equals cell fraction numerator 8 x squared minus x squared plus 1 over denominator open parentheses x plus 1 close parentheses open parentheses 4 x close parentheses end fraction end cell row blank equals cell fraction numerator 7 x squared plus 1 over denominator 4 x squared plus 4 x end fraction end cell end table 

  • f open parentheses x close parentheses equals fraction numerator 2 x over denominator x plus 1 end fraction terdefinisi apabila nilai x not equal to negative 1 maka D subscript f equals open curly brackets x vertical line space x not equal to negative 1 comma space x element of straight real numbers close curly brackets 
  • g open parentheses x close parentheses equals fraction numerator x minus 1 over denominator 4 x end fraction terdefinisi apabila nilai x not equal to 0 maka D subscript g equals open curly brackets x vertical line space x not equal to 0 comma space x element of straight real numbers close curly brackets 

table attributes columnalign right center left columnspacing 0px end attributes row cell D subscript f plus g end subscript end cell equals cell D subscript f intersection D subscript g end cell row blank equals cell open curly brackets x vertical line space x not equal to negative 1 space comma space x element of straight real numbers close curly brackets intersection open curly brackets x space vertical line x not equal to 0 space comma space x element of straight real numbers close curly brackets end cell row blank equals cell open curly brackets x vertical line space x not equal to negative 1 space dan space x not equal to 0 comma space x element of straight real numbers close curly brackets end cell end table 

10

5.0 (1 rating)

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