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Perhatikan gambar diagram kartesius berikut ini!   Domain dari fungsi di atas adalah ....

Pertanyaan

Perhatikan gambar diagram kartesius berikut ini!



 

Domain dari fungsi di atas adalah ....

  1. D subscript f equals open curly brackets x vertical line x element of straight real numbers close curly brackets 

  2. D subscript f equals open curly brackets x vertical line x not equal to 0 comma space x element of straight real numbers close curly brackets 

  3. D subscript f equals open curly brackets x vertical line x not equal to 0 comma space x element of straight natural numbers close curly brackets 

  4. D subscript f equals open curly brackets x vertical line x not equal to 0 comma space x element of straight integer numbers close curly brackets 

  5. D subscript f equals open curly brackets x vertical line x element of straight integer numbers close curly brackets 

Pembahasan Soal:

Pada gambar di atas, grafik fungsi dinyatakan dengan garis penuh (tidak terputus-putus) sehingga domainnya berupa bilangan real.

Perhatikan bahwa saat x equals 0, terdapat tanda bulatan kosong yang menunjukkan bahwa 0 tidak termasuk dalam domain.

Jadi, domain dari fungsi di atas adalah D subscript f equals open curly brackets x vertical line x not equal to 0 comma space x element of straight real numbers close curly brackets.

Dengan demikian, jawaban yang tepat adalah B.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

A. Acfreelance

Terakhir diupdate 01 Mei 2021

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Pertanyaan yang serupa

Diberikan dua buah fungsi  dan . Tentukan rumus fungsi , , dan , serta selanjutnya tentukan domain dari fungsi yang baru terbentuk!

Pembahasan Soal:

Ingat!

Fungsi adalah pemetaan setiap anggota sebuah himpunan (yang dinamakan sebagai domain atau daerah asal) kepada anggota himpunan yang lain (yang dinamakan sebagai kodomain atau daerah kawan).

Operasi pada dua fungsi seperti berikut.

(f+g)(x)(fg)(x)(gf)(x)===f(x)+g(x)f(x)g(x)g(x)f(x)

Sehingga, diperoleh perhitungan berikut.

f(x)=(x24)Df=(,3)(3,)g(x)=2x3Dg=(,)

(f+g)(x)Df+gDf+gDf+g====(x24)+2x3DfDg(,3)(3,)(,)(,3)(3,)

Fungsi (f+g)(x) tidak mempunyai batas domain, sehingga domain fungsi tersebut <x<.

(fg)(x)(fg)(x)DfgDfgDfg=====f(x)g(x)((x24))(2x3)DfDg(,3)(3,)(,)(,3)(3,)

Fungsi (fg)(x)  tidak mempunyai batas domain, sehingga domain fungsi tersebut <x<.

(gf)(x)(gf)(x)D(gf)D(gf)D(gf)D(gf)======g(x)f(x)(2x3)(x24)DfDg{x=23}(,3)(3,)(,){x=23}(,3)(3,){x=23}(,3)(3,)

Fungsi (gf)(x) memiliki batas-batas yaitu 2x3>02x>3x>23 dan 2x3<02x<3x<23 , sehingga domain fungsi tersebut <23dan23<x<.

Roboguru

Diberikan dua buah fungsi  dan . Tentukan rumus fungsi , , dan , serta selanjutnya tentukan domain dari fungsi yang baru terbentuk!

Pembahasan Soal:

begin mathsize 14px style f left parenthesis x right parenthesis equals fraction numerator 2 over denominator x minus 3 end fraction straight D subscript f equals left curly bracket x space left enclose space x not equal to 3 comma space x element of straight real numbers end enclose right curly bracket  g left parenthesis x right parenthesis equals 6 x plus 5 straight D subscript g equals left curly bracket x space left enclose space x element of straight real numbers end enclose right curly bracket  left parenthesis f plus g right parenthesis left parenthesis x right parenthesis equals f left parenthesis x right parenthesis plus g left parenthesis x right parenthesis left parenthesis f plus g right parenthesis left parenthesis x right parenthesis equals fraction numerator 2 over denominator x minus 3 end fraction plus 6 x plus 5 left parenthesis f plus g right parenthesis left parenthesis x right parenthesis equals fraction numerator 2 plus 6 x left parenthesis x minus 3 right parenthesis plus 5 left parenthesis x minus 3 right parenthesis over denominator x minus 3 end fraction left parenthesis f plus g right parenthesis left parenthesis x right parenthesis equals fraction numerator 2 plus 6 x squared minus 18 x plus 5 x minus 15 over denominator x minus 3 end fraction left parenthesis f plus g right parenthesis left parenthesis x right parenthesis equals fraction numerator 6 x squared minus 13 x minus 13 over denominator x minus 3 end fraction straight D subscript f plus g end subscript equals straight D subscript f intersection straight D subscript g straight D subscript f plus g end subscript equals left parenthesis negative infinity comma 3 right parenthesis union left parenthesis 3 comma infinity right parenthesis intersection left parenthesis negative infinity comma infinity right parenthesis straight D subscript f plus g end subscript equals left parenthesis negative infinity comma 3 right parenthesis union left parenthesis 3 comma infinity right parenthesis  left parenthesis f times g right parenthesis left parenthesis x right parenthesis equals f left parenthesis x right parenthesis times g left parenthesis x right parenthesis left parenthesis f times g right parenthesis left parenthesis x right parenthesis equals left parenthesis fraction numerator 2 over denominator x minus 3 end fraction right parenthesis times left parenthesis 6 x plus 5 right parenthesis left parenthesis f times g right parenthesis left parenthesis x right parenthesis equals fraction numerator 2 left parenthesis 6 x plus 5 right parenthesis over denominator x minus 3 end fraction left parenthesis f times g right parenthesis left parenthesis x right parenthesis equals fraction numerator 12 x plus 10 over denominator x minus 3 end fraction straight D subscript f times g end subscript equals straight D subscript f intersection straight D subscript g straight D subscript f times g end subscript equals left parenthesis negative infinity comma 3 right parenthesis union left parenthesis 3 comma infinity right parenthesis intersection left parenthesis negative infinity comma infinity right parenthesis straight D subscript f times g end subscript equals left parenthesis negative infinity comma 3 right parenthesis union left parenthesis 3 comma infinity right parenthesis  open parentheses f over g close parentheses left parenthesis x right parenthesis equals fraction numerator f left parenthesis x right parenthesis over denominator g left parenthesis x right parenthesis end fraction open parentheses f over g close parentheses left parenthesis x right parenthesis equals left parenthesis fraction numerator 2 over denominator x minus 3 end fraction right parenthesis divided by left parenthesis 6 x plus 5 right parenthesis open parentheses f over g close parentheses left parenthesis x right parenthesis equals fraction numerator 2 over denominator left parenthesis x minus 3 right parenthesis left parenthesis 6 x plus 5 right parenthesis end fraction straight D subscript open parentheses f over g close parentheses end subscript equals straight D subscript f intersection straight D subscript g minus open curly brackets x equals 3 comma space x equals negative 5 over 6 close curly brackets straight D subscript open parentheses straight f over straight g close parentheses end subscript equals left parenthesis negative infinity comma 3 right parenthesis union left parenthesis 3 comma infinity right parenthesis intersection left parenthesis negative infinity comma infinity right parenthesis minus open curly brackets x equals 3 comma space x equals negative 5 over 6 close curly brackets straight D subscript open parentheses straight f over straight g close parentheses end subscript equals left parenthesis negative infinity comma 3 right parenthesis union left parenthesis 3 comma infinity right parenthesis minus open curly brackets x equals 3 comma space x equals negative 5 over 6 close curly brackets straight D subscript open parentheses f over g close parentheses end subscript equals left parenthesis negative infinity comma negative 5 over 6 right parenthesis union left parenthesis negative 5 over 6 comma 3 right parenthesis union left parenthesis 3 comma infinity right parenthesis end style       

Roboguru

Diberikan dua buah fungsi  dan . Tentukan rumus fungsi , , dan , serta selanjutnya tentukan domain dari fungsi yang baru terbentuk!

Pembahasan Soal:

begin mathsize 14px style f left parenthesis x right parenthesis equals square root of x straight D subscript f equals left square bracket 0 comma infinity right parenthesis  g left parenthesis x right parenthesis equals square root of x squared minus 1 end root straight D subscript g equals left parenthesis negative infinity comma negative 1 right square bracket union left square bracket 1 comma infinity right parenthesis  left parenthesis f plus g right parenthesis left parenthesis x right parenthesis equals f left parenthesis x right parenthesis plus g left parenthesis x right parenthesis left parenthesis f plus g right parenthesis left parenthesis x right parenthesis equals square root of x plus square root of x squared minus 1 end root straight D subscript f plus g end subscript equals straight D subscript f intersection straight D subscript g straight D subscript f plus g end subscript equals left square bracket 0 comma infinity right parenthesis intersection left parenthesis negative infinity comma negative 1 right square bracket union left square bracket 1 comma infinity right parenthesis straight D subscript f plus g end subscript equals left square bracket 1 comma infinity right parenthesis  left parenthesis f times g right parenthesis left parenthesis x right parenthesis equals f left parenthesis x right parenthesis times g left parenthesis x right parenthesis left parenthesis f times g right parenthesis left parenthesis x right parenthesis equals square root of x open parentheses x squared minus 1 close parentheses end root left parenthesis f times g right parenthesis left parenthesis x right parenthesis equals square root of x cubed minus x end root straight D subscript f times g end subscript equals straight D subscript f intersection straight D subscript g straight D subscript f times g end subscript equals left square bracket 0 comma infinity right parenthesis intersection left parenthesis negative infinity comma negative 1 right square bracket union left square bracket 1 comma infinity right parenthesis straight D subscript f times g end subscript equals left square bracket 1 comma infinity right parenthesis  open parentheses f over g close parentheses left parenthesis x right parenthesis equals fraction numerator f left parenthesis x right parenthesis over denominator g left parenthesis x right parenthesis end fraction open parentheses f over g close parentheses left parenthesis x right parenthesis equals fraction numerator square root of x over denominator square root of x squared minus 1 end root end fraction open parentheses f over g close parentheses left parenthesis x right parenthesis equals square root of fraction numerator x over denominator x squared minus 1 end fraction end root straight D subscript open parentheses f over g close parentheses end subscript equals D subscript f intersection D subscript g minus open curly brackets x equals plus-or-minus 1 close curly brackets straight D subscript open parentheses f over g close parentheses end subscript equals left square bracket 0 comma infinity right parenthesis intersection left parenthesis negative infinity comma negative 1 right square bracket union left square bracket 1 comma infinity right parenthesis minus open curly brackets x equals plus-or-minus 1 close curly brackets straight D subscript open parentheses f over g close parentheses end subscript equals left square bracket 1 comma infinity right parenthesis minus open curly brackets x equals plus-or-minus 1 close curly brackets straight D subscript open parentheses f over g close parentheses end subscript equals left parenthesis 1 comma infinity right parenthesis  end style  

Roboguru

Diberikan dua buah fungsi  dan . Tentukan rumus fungsi , , dan , serta selanjutnya tentukan domain dari fungsi yang baru terbentuk!

Pembahasan Soal:

begin mathsize 14px style f left parenthesis x right parenthesis equals fraction numerator 1 over denominator square root of x end fraction straight D subscript f equals left parenthesis 0 comma infinity right parenthesis  g left parenthesis x right parenthesis equals fraction numerator 2 over denominator square root of x squared end root end fraction straight D subscript g equals left parenthesis 0 comma infinity right parenthesis  left parenthesis f plus g right parenthesis left parenthesis x right parenthesis equals f left parenthesis x right parenthesis plus g left parenthesis x right parenthesis left parenthesis f plus g right parenthesis left parenthesis x right parenthesis equals fraction numerator 1 over denominator square root of x end fraction plus fraction numerator 2 over denominator square root of x squared end root end fraction straight D subscript f plus g end subscript equals straight D subscript f intersection straight D subscript g straight D subscript f plus g end subscript equals left parenthesis 0 comma infinity right parenthesis intersection left parenthesis 0 comma infinity right parenthesis straight D subscript f plus g end subscript equals left parenthesis 0 comma infinity right parenthesis  left parenthesis f times g right parenthesis left parenthesis x right parenthesis equals f left parenthesis x right parenthesis times g left parenthesis x right parenthesis left parenthesis f times g right parenthesis left parenthesis x right parenthesis equals fraction numerator 1 over denominator square root of x end fraction times fraction numerator 2 over denominator square root of x squared end root end fraction left parenthesis f times g right parenthesis left parenthesis x right parenthesis equals fraction numerator 2 over denominator square root of x cubed end root end fraction straight D subscript f times g end subscript equals straight D subscript f intersection straight D subscript g straight D subscript f times g end subscript equals left parenthesis 0 comma infinity right parenthesis intersection left parenthesis 0 comma infinity right parenthesis straight D subscript f times g end subscript equals left parenthesis 0 comma infinity right parenthesis  open parentheses f over g close parentheses left parenthesis x right parenthesis equals fraction numerator f left parenthesis x right parenthesis over denominator g left parenthesis x right parenthesis end fraction open parentheses f over g close parentheses left parenthesis x right parenthesis equals fraction numerator 1 over denominator square root of x end fraction divided by fraction numerator 2 over denominator square root of x squared end root end fraction open parentheses f over g close parentheses left parenthesis x right parenthesis equals fraction numerator square root of x squared end root over denominator 2 square root of x end fraction open parentheses f over g close parentheses left parenthesis x right parenthesis equals fraction numerator square root of x over denominator 2 end fraction straight D subscript open parentheses f over g close parentheses end subscript equals straight D subscript f intersection straight D subscript g straight D subscript open parentheses f over g close parentheses end subscript equals left parenthesis 0 comma infinity right parenthesis intersection left parenthesis 0 comma infinity right parenthesis straight D subscript open parentheses f over g close parentheses end subscript equals left parenthesis 0 comma infinity right parenthesis  end style  

Roboguru

Diberikan dua buah fungsi  dan . Tentukan rumus fungsi , , dan , serta selanjutnya tentukan domain dari fungsi yang baru terbentuk!

Pembahasan Soal:

begin mathsize 14px style f left parenthesis x right parenthesis equals fraction numerator 1 over denominator x minus 1 end fraction straight D subscript f equals left parenthesis negative infinity comma 1 right parenthesis union left parenthesis 1 comma infinity right parenthesis  g left parenthesis x right parenthesis equals fraction numerator x over denominator 2 x minus 1 end fraction straight D subscript g equals open parentheses negative infinity comma 1 half close parentheses union open parentheses 1 half comma infinity close parentheses  open parentheses f plus g close parentheses left parenthesis x right parenthesis equals f left parenthesis x right parenthesis plus g left parenthesis x right parenthesis open parentheses f plus g close parentheses left parenthesis x right parenthesis equals fraction numerator 1 over denominator x minus 1 end fraction plus fraction numerator x over denominator 2 x minus 1 end fraction open parentheses f plus g close parentheses left parenthesis x right parenthesis equals fraction numerator 1 open parentheses 2 x minus 1 close parentheses plus x open parentheses x minus 1 close parentheses over denominator open parentheses x minus 1 close parentheses open parentheses 2 x minus 1 close parentheses end fraction open parentheses f plus g close parentheses left parenthesis x right parenthesis equals fraction numerator open parentheses 2 x minus 1 close parentheses plus x squared minus x over denominator open parentheses x minus 1 close parentheses open parentheses 2 x minus 1 close parentheses end fraction open parentheses f plus g close parentheses left parenthesis x right parenthesis equals fraction numerator x squared plus x minus 1 over denominator open parentheses x minus 1 close parentheses open parentheses 2 x minus 1 close parentheses end fraction straight D subscript f plus g end subscript equals straight D subscript f intersection straight D subscript g straight D subscript f plus g end subscript equals left parenthesis negative infinity comma 1 right parenthesis union left parenthesis 1 comma infinity right parenthesis intersection open parentheses negative infinity comma 1 half close parentheses union open parentheses 1 half comma infinity close parentheses straight D subscript f plus g end subscript equals open parentheses negative infinity comma 1 half close parentheses union open parentheses 1 half comma 1 close parentheses union left parenthesis 1 comma infinity right parenthesis  open parentheses f times g close parentheses left parenthesis x right parenthesis equals f left parenthesis x right parenthesis times g left parenthesis x right parenthesis open parentheses f times g close parentheses left parenthesis x right parenthesis equals fraction numerator 1 over denominator x minus 1 end fraction times fraction numerator x over denominator 2 x minus 1 end fraction open parentheses f times g close parentheses left parenthesis x right parenthesis equals fraction numerator x over denominator open parentheses x minus 1 close parentheses open parentheses 2 x minus 1 close parentheses end fraction straight D subscript f times g end subscript equals straight D subscript f intersection straight D subscript g straight D subscript f times g end subscript equals left parenthesis negative infinity comma 1 right parenthesis union left parenthesis 1 comma infinity right parenthesis intersection open parentheses negative infinity comma 1 half close parentheses union open parentheses 1 half comma infinity close parentheses straight D subscript f times g end subscript equals open parentheses negative infinity comma 1 half close parentheses union open parentheses 1 half comma 1 close parentheses union left parenthesis 1 comma infinity right parenthesis  open parentheses f over g close parentheses left parenthesis x right parenthesis equals fraction numerator f left parenthesis x right parenthesis over denominator g left parenthesis x right parenthesis end fraction open parentheses f over g close parentheses left parenthesis x right parenthesis equals fraction numerator 1 over denominator x minus 1 end fraction divided by fraction numerator x over denominator 2 x minus 1 end fraction open parentheses f over g close parentheses left parenthesis x right parenthesis equals fraction numerator open parentheses 2 x minus 1 close parentheses over denominator x open parentheses x minus 1 close parentheses end fraction straight D subscript open parentheses f over g close parentheses end subscript equals straight D subscript f intersection straight D subscript g minus open curly brackets x equals 0 comma space x equals 1 close curly brackets straight D subscript open parentheses f over g close parentheses end subscript equals left parenthesis negative infinity comma 1 right parenthesis union left parenthesis 1 comma infinity right parenthesis intersection open parentheses negative infinity comma 1 half close parentheses union open parentheses 1 half comma infinity close parentheses minus open curly brackets x equals 0 comma space x equals 1 close curly brackets straight D subscript open parentheses f over g close parentheses end subscript equals open parentheses negative infinity comma 0 close parentheses union open parentheses 0 comma 1 half close parentheses union open parentheses 1 half comma 1 close parentheses union left parenthesis 1 comma infinity right parenthesis    end style  

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