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Diketahui f(x)=x+2 dan g(x)=x2−7, Tentukan (f+g)(x)!

Pertanyaan

Diketahui begin mathsize 14px style f open parentheses x close parentheses equals x plus 2 end style dan begin mathsize 14px style g open parentheses x close parentheses equals x squared minus 7 end style, Tentukan begin mathsize 14px style open parentheses f plus g close parentheses open parentheses x close parentheses end style!

Pembahasan Soal:

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 x plus 2 plus open parentheses x squared minus 7 close parentheses end cell row blank equals cell x squared plus x minus 5 end cell end table end style

Jadi, begin mathsize 14px style open parentheses f plus g close parentheses open parentheses x close parentheses equals x squared plus x minus 5 end style.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

R. Bella

Mahasiswa/Alumni UIN Syarif Hidayatullah Jakarta

Terakhir diupdate 07 Oktober 2021

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Pertanyaan yang serupa

Jika diketahui f(x)=x−26​ dan g(x)=4x, hasil dari fungsi (f+g)(x) adalah ....

Pembahasan Soal:

Hasil dari fungsi dapat dicari dengan menjumlahkan kedua fungsi sebagai berikut.

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 fraction numerator 6 over denominator x minus 2 end fraction plus 4 x end cell row blank equals cell fraction numerator 6 plus 4 x squared minus 8 x over denominator x minus 2 end fraction end cell end table end style

Jadi, hasil dari begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis f plus g right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis x right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 6 plus 4 x squared minus 8 x over denominator x minus 2 end fraction end cell end table end style.

0

Roboguru

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

Pembahasan Soal:

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 

 

 

0

Roboguru

Diketahui f:R→R yang formulanya ditentukan oleh: f(x)={x2−x;x≥1x+2;x<1​nilai f(4)+f(2)−f(0)=...

Pembahasan Soal:

begin mathsize 14px style f left parenthesis x right parenthesis equals x squared minus x semicolon x greater or equal than 1 f left parenthesis x right parenthesis equals x plus 2 semicolon x less than 1 end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis 4 right parenthesis plus f left parenthesis 2 right parenthesis minus f left parenthesis 0 right parenthesis end cell equals cell left parenthesis 4 squared minus 4 right parenthesis plus left parenthesis 2 squared minus 2 right parenthesis minus left parenthesis 0 plus 2 right parenthesis end cell row blank equals cell left parenthesis 16 minus 4 right parenthesis plus left parenthesis 4 minus 2 right parenthesis minus 2 end cell row blank equals cell 12 plus 2 minus 2 end cell row blank equals 12 end table end style 

Jadi, jawaban yang tepat adalah D.

0

Roboguru

Diekatahui , dan . Hasil dari: a. (f+g)(x)=...

Pembahasan Soal:

Ingat bahwa:

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 ,

Sehingga:

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 open parentheses 2 x squared minus 4 close parentheses plus open parentheses 3 x squared minus 2 x close parentheses end cell row blank equals cell 5 x squared minus 2 x minus 4 end cell end table

Jadi, open parentheses f plus g close parentheses open parentheses x close parentheses adalah 5 x squared minus 2 x minus 4

0

Roboguru

Tentukan rumus fungsi (f+g)(x),(f⋅g)(x),(gf​)(x) dan daerah asalnya, jika diketahui f(x) dan g(x) berikut: f(x)=x2−16​dang(x)=2x+6​1​

Pembahasan Soal:

Diketahui : begin mathsize 14px style f left parenthesis x right parenthesis equals square root of x squared minus 16 end root space dan space g left parenthesis x right parenthesis equals fraction numerator 1 over denominator square root of 2 x plus 6 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 square root of x squared minus 16 end root plus fraction numerator 1 over denominator square root of 2 x plus 6 end root end fraction 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 end cell equals cell open curly brackets right enclose x space x squared minus 16 greater or equal than 0 close curly brackets end cell row blank equals cell open curly brackets right enclose x space open parentheses x plus 4 close parentheses open parentheses x minus 4 close parentheses greater or equal than 0 comma space x element of straight real numbers close curly brackets end cell row blank equals cell open curly brackets right enclose x space x less or equal than negative 4 space atau space x greater or equal than 4 comma space x element of straight real numbers close curly brackets end cell row cell D subscript g end cell equals cell open curly brackets right enclose x space 2 x plus 6 greater than 0 close curly brackets end cell row blank equals cell open curly brackets right enclose x space x greater than negative 3 comma space x element of straight real numbers close curly brackets end cell row blank blank blank end table 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 space x less or equal than negative 4 space atau space x greater or equal than 4 comma space x element of straight real numbers close curly brackets intersection open curly brackets right enclose x space x greater than negative 3 comma space x element of straight real numbers close curly brackets end cell row blank equals cell open curly brackets right enclose x space x greater-than or slanted equal to 4 comma space x element of straight real numbers close curly brackets 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 square root of x squared minus 16 end root times fraction numerator 1 over denominator square root of 2 x plus 6 end root end fraction end cell row blank equals cell fraction numerator square root of x squared minus 16 end root over denominator square root of 2 x plus 6 end root end fraction times fraction numerator square root of 2 x plus 6 end root over denominator square root of 2 x plus 6 end root end fraction end cell row blank equals cell fraction numerator 1 over denominator 2 x plus 6 end fraction square root of open parentheses x squared minus 16 close parentheses open parentheses 2 x plus 6 close parentheses end root end cell row blank equals cell fraction numerator 1 over denominator 2 x plus 6 end fraction square root of 2 x cubed plus 6 x squared minus 32 x minus 96 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 end cell equals cell open curly brackets right enclose x space x squared minus 16 greater or equal than 0 close curly brackets end cell row blank equals cell open curly brackets right enclose x space open parentheses x plus 4 close parentheses open parentheses x minus 4 close parentheses greater or equal than 0 comma space x element of straight real numbers close curly brackets end cell row blank equals cell open curly brackets right enclose x space x less or equal than negative 4 space atau space x greater or equal than 4 comma space x element of straight real numbers close curly brackets end cell row cell D subscript g end cell equals cell open curly brackets right enclose x space 2 x plus 6 greater than 0 close curly brackets end cell row blank equals cell open curly brackets right enclose x space x greater than negative 3 comma space x element of straight real numbers close curly brackets end cell row blank blank blank end table 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 left curly bracket right enclose x space x less or equal than negative 4 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 space x greater than negative 3 comma space x element of straight real numbers right curly bracket end cell row blank equals cell left curly bracket right enclose x space x greater-than or slanted equal to 4 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 square root of x squared minus 16 end root divided by fraction numerator 1 over denominator square root of 2 x plus 6 end root end fraction end cell row blank equals cell square root of x squared minus 16 end root times square root of 2 x plus 6 end root end cell row blank equals cell square root of 2 x cubed plus 6 x squared minus 32 x minus 96 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 f end cell equals cell open curly brackets right enclose x space x squared minus 16 greater or equal than 0 close curly brackets end cell row blank equals cell open curly brackets right enclose x space open parentheses x plus 4 close parentheses open parentheses x minus 4 close parentheses greater or equal than 0 comma space x element of straight real numbers close curly brackets end cell row blank equals cell open curly brackets right enclose x space x less or equal than negative 4 space atau space x greater or equal than 4 comma space x element of straight real numbers close curly brackets end cell row cell D subscript g end cell equals cell open curly brackets right enclose x space 2 x plus 6 greater than 0 close curly brackets end cell row blank equals cell open curly brackets right enclose x space x greater than negative 3 comma space x element of straight real numbers close curly brackets end cell row blank blank blank end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell D subscript f over g end subscript end cell equals cell D subscript f intersection D subscript g space comma space g open parentheses x close parentheses not equal to 0 end cell row blank equals cell left curly bracket right enclose x space x less or equal than negative 4 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 space x greater than negative 3 comma space x element of straight real numbers right curly bracket comma space x not equal to negative 3 end cell row blank equals cell left curly bracket right enclose x space x greater-than or slanted equal to 4 comma space x element of straight real numbers right curly bracket end cell end table end style 

 

 

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Roboguru

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