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 ) = x 2 − x − 8 ​ dan g ( x ) = x + 8 ​ 1 ​

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

   

M. Mariyam

Master Teacher

Mahasiswa/Alumni Institut Pertanian Bogor

Jawaban terverifikasi

Pembahasan

Sebelum menjawab soal di atas, kita asumsikan bahwa , supaya persamaan di dalam akar dapat difaktorkan. sehingga jika , maka a. Daerah asal adalah b. Daerah asal adalah c. Daerah asal adalah

Sebelum menjawab soal di atas, kita asumsikan bahwa begin mathsize 14px style f open parentheses x close parentheses equals square root of x squared minus 2 x minus 8 end root end style , supaya persamaan di dalam akar dapat difaktorkan. sehingga 

jika begin mathsize 14px style f left parenthesis x right parenthesis equals square root of x squared minus 2 x minus 8 end root space dan space g left parenthesis x right parenthesis equals fraction numerator 1 over denominator square root of x plus 8 end root end fraction end style, maka

a. begin mathsize 14px style open parentheses f plus g close parentheses left parenthesis x right parenthesis end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis f plus g right parenthesis left parenthesis x right parenthesis end cell equals cell f left parenthesis x right parenthesis plus g left parenthesis x right parenthesis end cell row blank equals cell square root of x squared minus 2 x minus 8 end root plus fraction numerator 1 over denominator square root of x plus 8 end root end fraction end cell end table end style  

Daerah asal begin mathsize 14px style open parentheses f plus g close parentheses left parenthesis x right parenthesis end style adalah

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b. begin mathsize 14px style left parenthesis f times g right parenthesis end style size 14px left parenthesis size 14px x size 14px right parenthesis 

table attributes columnalign right center left columnspacing 0px end attributes row cell size 14px left parenthesis size 14px f size 14px times size 14px g size 14px right parenthesis size 14px left parenthesis size 14px x size 14px right parenthesis end cell size 14px equals cell size 14px f size 14px left parenthesis size 14px x size 14px right parenthesis size 14px times size 14px g size 14px left parenthesis size 14px x size 14px right parenthesis end cell row blank size 14px equals cell square root of size 14px x to the power of size 14px 2 size 14px minus size 14px 2 size 14px x size 14px minus size 14px 8 end root size 14px. fraction numerator size 14px 1 over denominator square root of size 14px x size 14px plus size 14px 8 end root end fraction end cell row blank size 14px equals cell square root of fraction numerator size 14px x to the power of size 14px 2 size 14px minus size 14px 2 size 14px x size 14px minus size 14px 8 over denominator size 14px x size 14px plus size 14px 8 end fraction end root end cell end table    

Daerah asal begin mathsize 14px style left parenthesis f times g right parenthesis end style size 14px left parenthesis size 14px x size 14px right parenthesis  adalah

 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell D subscript f end cell equals cell left curly bracket right enclose x x squared minus 2 x minus 8 greater or equal than 0 comma space x element of straight real numbers right curly bracket end cell row blank equals cell left curly bracket right enclose x open parentheses x minus 4 close parentheses open parentheses x plus 2 close parentheses greater or equal than 0 comma space x element of straight real numbers right curly bracket end cell row blank equals cell left curly bracket right enclose x x less or equal than negative 2 space atau space x greater or equal than 4 comma space x element of straight real numbers right curly bracket end cell row cell D subscript g end cell equals cell left curly bracket right enclose x x plus 8 greater than 0 comma space x element of straight real numbers right curly bracket end cell row blank equals cell left curly bracket right enclose x x greater than negative 8 comma space x element of straight real numbers right curly bracket end cell 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 left curly bracket right enclose x x less or equal than negative 2 space atau space x greater or equal than 4 comma space x element of straight real numbers right curly bracket intersection left curly bracket right enclose x x greater than negative 8 comma space x element of straight real numbers right curly bracket end cell row blank equals cell left curly bracket right enclose x minus 8 less than x less or equal than negative 2 space atau space x greater or equal than 4 comma space x element of straight real numbers right curly bracket end cell row blank blank blank end table end style 

 c. 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 open parentheses f over g close parentheses open parentheses x close parentheses end cell equals cell fraction numerator f left parenthesis x right parenthesis over denominator g left parenthesis x right parenthesis end fraction end cell row blank equals cell square root of x squared minus 2 x minus 8 end root divided by fraction numerator 1 over denominator square root of x plus 8 end root end fraction end cell row blank equals cell square root of x squared minus 2 x minus 8 end root times square root of x plus 8 end root end cell row blank equals cell square root of x cubed plus 6 x squared minus 24 x minus 64 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  adalah

 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell D subscript f end cell equals cell left curly bracket right enclose x x squared minus 2 x minus 8 greater or equal than 0 comma space x element of straight real numbers right curly bracket end cell row blank equals cell left curly bracket right enclose x left parenthesis x minus 4 right parenthesis left parenthesis x plus 2 right parenthesis greater or equal than 0 comma space x element of straight real numbers right curly bracket end cell row blank equals cell left curly bracket right enclose x x less or equal than negative 2 space atau space x greater or equal than 4 comma space x element of straight real numbers right curly bracket end cell row cell D subscript g end cell equals cell left curly bracket right enclose x x plus 8 greater than 0 comma space x element of straight real numbers right curly bracket end cell row blank equals cell left curly bracket right enclose x x greater than negative 8 comma space x element of straight real numbers right curly bracket end cell row cell D subscript f over g end subscript end cell equals cell D subscript f intersection D subscript g comma space g not equal to 0 end cell row blank equals cell left curly bracket right enclose x x less or equal than negative 2 space atau space x greater or equal than 4 comma space x element of straight real numbers right curly bracket intersection left curly bracket right enclose x x greater than negative 8 comma space x element of straight real numbers right curly bracket comma space x not equal to negative 8 end cell row blank equals cell left curly bracket right enclose x minus 8 less than x less or equal than negative 2 space atau space x greater or equal than 4 comma space x element of straight real numbers right curly bracket end cell row blank blank blank end table end style 

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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 ) = x 2 − 16 ​ dan g ( x ) = 2 x + 6 ​ 1 ​

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