Pertanyaan

Tentukan rumus fungsi ( f + g ) ( x ) , ( f ⋅ g ) ( x ) , ( g f ​ ) ( x ) dan daerah asalnya, jika diketahui f ( x ) dan g ( x ) berikut: f ( x ) = 3 x − 6 dan g ( x ) = x − 3 ​ 1 ​

Tentukan rumus fungsi  dan daerah asalnya, jika diketahui  dan  berikut:

 

M. Mariyam

Master Teacher

Mahasiswa/Alumni Institut Pertanian Bogor

Jawaban terverifikasi

Pembahasan

Diketahui : Ditanyakan: dan daerah asalnya Jawab: a. daerah asal : b. daerah asal : c. Daerah asal :

Diketahui : begin mathsize 14px style f open parentheses x close parentheses equals 3 x minus 6 space dan space g open parentheses x close parentheses equals fraction numerator 1 over denominator square root of x minus 3 end root end fraction end style

Ditanyakan: begin mathsize 14px style open parentheses f plus g close parentheses open parentheses x close parentheses comma space open parentheses f times g close parentheses open parentheses x close parentheses comma space open parentheses f over g close parentheses open parentheses x close parentheses end style dan daerah asalnya

Jawab:

a.

begin mathsize 14px style 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 3 x minus 6 plus fraction numerator 1 over denominator square root of x minus 3 end root end fraction end cell row blank equals cell 3 x plus fraction numerator 1 over denominator square root of x minus 3 end root end fraction minus 6 end cell end table end style 

daerah asal begin mathsize 14px style open parentheses f plus g close parentheses open parentheses x close parentheses end style :

 begin mathsize 14px style 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 right enclose x x element of straight real numbers intersection space x minus 3 greater than 0 close curly brackets end cell row blank equals cell open curly brackets right enclose x x element of straight real numbers intersection x greater than 3 close curly brackets end cell row blank equals cell left curly bracket right enclose x x greater than 3 comma space x element of straight real numbers right curly bracket end cell end table end style  

b. 

begin mathsize 14px style 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 3 x minus 6 close parentheses open parentheses fraction numerator 1 over denominator square root of x minus 3 end root end fraction close parentheses end cell row blank equals cell fraction numerator 3 x minus 6 over denominator square root of x minus 3 end root end fraction end cell row blank equals cell fraction numerator 3 x minus 6 over denominator square root of x minus 3 end root end fraction times fraction numerator square root of x minus 3 end root over denominator square root of x minus 3 end root end fraction end cell row blank equals cell fraction numerator 3 open parentheses x minus 2 close parentheses over denominator x minus 3 end fraction square root of x minus 3 end root end cell row blank equals cell 3 fraction numerator x minus 2 over denominator x minus 3 end fraction square root of x minus 3 end root end cell end table end style 

daerah asal begin mathsize 14px style open parentheses f. g close parentheses open parentheses x close parentheses end style :

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell D subscript f times g end subscript end cell equals cell D subscript f intersection D subscript g end cell row blank equals cell open curly brackets right enclose x x element of straight real numbers intersection space x minus 3 greater than 0 close curly brackets end cell row blank equals cell open curly brackets right enclose x x element of straight real numbers intersection x greater than 3 close curly brackets end cell row blank equals cell left curly bracket right enclose x x greater than 3 comma space x element of straight real numbers right curly bracket end cell end table end style  

c.

begin mathsize 14px style 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 open parentheses 3 x minus 6 close parentheses divided by fraction numerator 1 over denominator square root of x minus 3 end root end fraction end cell row blank equals cell open parentheses 3 x minus 6 close parentheses square root of x minus 3 end root end cell row blank equals cell 3 open parentheses x minus 2 close parentheses square root of x minus 3 end root end cell end table end style  

Daerah asal begin mathsize 14px style open parentheses f over g close parentheses open parentheses x close parentheses end style :

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell D subscript blank subscript f over g end subscript end cell equals cell D subscript f intersection D subscript g comma space g open parentheses x close parentheses not equal to 0 end cell row blank equals cell left curly bracket right enclose x x element of straight real numbers intersection space x minus 3 greater than 0 right curly bracket comma space x minus 3 not equal to 0 end cell row blank equals cell left curly bracket right enclose x x element of straight real numbers intersection x greater than 3 right curly bracket comma space x not equal to 3 end cell row blank equals cell left curly bracket right enclose x x greater than 3 comma space x element of straight real numbers right curly bracket end cell end table end style 

 

 

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