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Pertanyaan

Diketahui fungsi begin mathsize 14px style f open parentheses x close parentheses equals 2 x plus 5 end style dan begin mathsize 14px style g open parentheses x close parentheses equals x squared minus 1 end style. Tentukan begin mathsize 14px style 3 f open parentheses x close parentheses end style!

Pembahasan Soal:

Untuk menentukan nilai begin mathsize 14px style 3 f open parentheses x close parentheses end style, kita hanya perlu mengalikan begin mathsize 14px style f open parentheses x close parentheses end style dengan begin mathsize 14px style 3 end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 3 f open parentheses x close parentheses end cell equals cell 3 open parentheses 2 x plus 5 close parentheses end cell row blank equals cell 6 x plus 15 end cell end table end style

Jadi, begin mathsize 14px style 3 f open parentheses x close parentheses equals 6 x plus 15 end style.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

F. Kartikasari

Mahasiswa/Alumni Universitas Negeri Surabaya

Terakhir diupdate 01 April 2021

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Pertanyaan yang serupa

Diketahui fungsi  dan . Jika , daerah asal fungsi  adalah ...

Pembahasan Soal:

Diketahui fungsi f open parentheses x close parentheses equals fraction numerator x plus 4 over denominator x minus 5 end fraction dan g open parentheses x close parentheses equals square root of x squared minus 9 x end root. Jika h open parentheses x close parentheses equals open parentheses f cross times g close parentheses open parentheses x close parentheses maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell h open parentheses x close parentheses end cell equals cell open parentheses f cross times g close parentheses open parentheses x close parentheses end cell row blank equals cell f open parentheses x close parentheses cross times g open parentheses x close parentheses end cell row blank equals cell fraction numerator x plus 4 over denominator x minus 5 end fraction open parentheses square root of x squared minus 9 x end root close parentheses end cell row blank equals cell fraction numerator open parentheses x plus 4 close parentheses square root of x squared minus 9 x end root over denominator x minus 5 end fraction end cell end table 

Supaya h open parentheses x close parentheses terdifinis maka penyebut tidak boleh sama dengan nol, sehingga pembuat nolnya adalah:

table attributes columnalign right center left columnspacing 0px end attributes row cell x minus 5 end cell equals 0 row x equals 5 end table

sehingga x not equal to 5, kemudian supaya square root of x squared minus 9 x end root terdefinisi maka:

x squared minus 9 x greater or equal than 0 x open parentheses x minus 9 close parentheses greater or equal than 0

diperoleh x greater or equal than 0 atau x greater or equal than 9, oleh karena jika x equals 1 diperoleh x squared minus 9 x less than 0 maka tidak memenuhi. 

Dengan demikian daerah asal fungsi h open parentheses x close parentheses adalah open curly brackets x vertical line x less or equal than 0 space atau space x greater or equal than 9 comma space x element of straight R close curly brackets.

Oleh karena itu, jawaban yang benar adalah D.

Roboguru

Fungsi  dan fungsi . Tentukanlah :  c.

Pembahasan Soal:

Dengan menerapkan sifat perkalian fungsi aljabar:

Error converting from MathML to accessible text.  

Jadi, Error converting from MathML to accessible text.

Roboguru

Misalkan diketahui  dan  dengan  dan , tentukan: c.

Pembahasan Soal:

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 x squared minus 8 x plus 12 close parentheses times open parentheses x minus 6 close parentheses end cell row blank equals cell x cubed minus 6 x squared minus 8 x squared plus 48 x plus 12 x minus 72 end cell row blank equals cell x cubed minus 14 x squared plus 60 x minus 72 end cell end table end style    

Roboguru

Diketahui fungsi  dan  . Hasil dari  adalah ...

Pembahasan Soal:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis f times g right parenthesis left parenthesis x right parenthesis end cell equals cell f left parenthesis x right parenthesis times g left parenthesis x right parenthesis end cell row blank equals cell open parentheses x squared minus 2 x plus 1 close parentheses times open parentheses 4 x minus 7 close parentheses end cell row blank equals cell 4 x cubed minus 7 x squared minus 8 x squared minus 14 x plus 4 x minus 7 end cell row blank equals cell 4 x cubed minus 15 x squared minus 10 x minus 7 end cell row cell left parenthesis f times g right parenthesis left parenthesis 3 right parenthesis end cell equals cell 4 left parenthesis 3 right parenthesis cubed minus 15 left parenthesis 3 right parenthesis squared minus 10 left parenthesis 3 right parenthesis minus 7 end cell row blank equals cell 108 minus 135 minus 30 minus 7 end cell row blank equals cell negative 64 end cell end table end style

Roboguru

Tentukan fungsi , ,  dan  dari fungsi-fungsi berikut: a.  dan

Pembahasan Soal:

  • 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.

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