Roboguru

Diberikan dua buah fungsi f(x)=2x−6 dan g(x)=8−4x. Tentukan rumus fungsi f+g, f⋅g, dan gf​, serta selanjutnya tentukan domain dari fungsi yang baru terbentuk!

Pertanyaan

Diberikan dua buah fungsi begin mathsize 14px style f left parenthesis x right parenthesis equals 2 x minus 6 end style dan begin mathsize 14px style g left parenthesis x right parenthesis equals 8 minus 4 x end style.

Tentukan rumus fungsi undefinedundefined, dan undefined, serta selanjutnya tentukan domain dari fungsi yang baru terbentuk!

Pembahasan Soal:

begin mathsize 14px style f left parenthesis x right parenthesis equals 2 x minus 6 straight D subscript f equals open curly brackets x space left enclose space x element of straight real numbers end enclose close curly brackets  g left parenthesis x right parenthesis equals 8 minus 4 x straight D subscript g equals open curly brackets x space left enclose space x element of straight real numbers end enclose close curly brackets  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 2 x minus 6 plus 8 minus 4 x left parenthesis f plus g right parenthesis left parenthesis x right parenthesis equals 2 minus 2 x straight D subscript f plus g end subscript equals open parentheses negative infinity comma infinity close parentheses intersection open parentheses negative infinity comma infinity close parentheses straight D subscript f plus g end subscript equals open parentheses negative infinity comma infinity close parentheses  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 open parentheses 2 x minus 6 close parentheses times open parentheses 8 minus 4 x close parentheses left parenthesis f times g right parenthesis left parenthesis x right parenthesis equals 16 x minus 8 x squared minus 48 plus 24 x left parenthesis f times g right parenthesis left parenthesis x right parenthesis equals negative 8 x squared plus 40 x minus 48 straight D subscript f times g end subscript equals open parentheses negative infinity comma infinity close parentheses intersection open parentheses negative infinity comma infinity close parentheses straight D subscript f times g end subscript equals open parentheses negative infinity comma infinity close parentheses  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 2 x minus 6 over denominator 8 minus 4 x end fraction open parentheses f over g close parentheses left parenthesis x right parenthesis equals fraction numerator 2 left parenthesis x minus 3 right parenthesis over denominator 2 left parenthesis 4 minus 2 x right parenthesis end fraction open parentheses f over g close parentheses left parenthesis x right parenthesis equals fraction numerator open parentheses x minus 3 close parentheses over denominator open parentheses 4 minus 2 x close parentheses end fraction straight D subscript f over g end subscript equals open parentheses negative infinity comma infinity close parentheses intersection open parentheses negative infinity comma infinity close parentheses minus open curly brackets x equals 2 close curly brackets space straight D subscript f over g end subscript equals open parentheses negative infinity comma 2 close parentheses union left parenthesis 2 comma infinity right parenthesis end style  

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

F. Fatimatuzzahroh

Mahasiswa/Alumni Institut Pertanian Bogor

Terakhir diupdate 05 Oktober 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Diberikan dua buah fungsi f(x)=x​ dan g(x)=(x2−1)​. Tentukan rumus fungsi f+g, f⋅g, dan gf​, 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  

0

Roboguru

Diberikan dua buah fungsi f(x)=2x+5 dan g(x)=x2. Tentukan rumus fungsi f+g, f⋅g, dan gf​, serta selanjutnya tentukan domain dari fungsi yang baru terbentuk!

Pembahasan Soal:

0

Roboguru

Diberikan dua buah fungsi f(x)=x​ dan g(x)=x2+1. Tentukan rumus fungsi f+g, f⋅g, dan gf​, 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 x squared plus 1 straight D subscript g equals left parenthesis negative infinity 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 x squared plus 1 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 infinity right parenthesis straight D subscript f plus g end subscript equals left square bracket 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 square root of x times open parentheses x squared plus 1 close parentheses 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 infinity right parenthesis straight D subscript f times g end subscript equals left square bracket 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 square root of x over denominator open parentheses x squared plus 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 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 infinity right parenthesis straight D subscript open parentheses f over g close parentheses end subscript equals left square bracket 0 comma infinity right parenthesis end style  

0

Roboguru

Diberikan dua buah fungsi f(x)=x−11​ dan g(x)=2x−1x​. Tentukan rumus fungsi f+g, f⋅g, dan gf​, 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  

0

Roboguru

Diberikan dua buah fungsi f(x)=4−2x2x−6​ dan g(x)=x+1​. Tentukan rumus fungsi f+g, f⋅g, dan gf​, 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 x minus 6 over denominator 4 minus 2 x end fraction straight D subscript f equals left curly bracket x space left enclose space x not equal to 2 comma space x element of straight real numbers end enclose right curly bracket  g left parenthesis x right parenthesis equals square root of x plus 1 end root straight D subscript g equals left curly bracket x space left enclose space x greater or equal than negative 1 comma 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 x minus 6 over denominator 4 minus 2 x end fraction plus square root of x plus 1 end root left parenthesis f plus g right parenthesis left parenthesis x right parenthesis equals fraction numerator left parenthesis x minus 3 right parenthesis over denominator left parenthesis 2 minus x right parenthesis end fraction plus square root of x plus 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 parenthesis negative infinity comma 2 right parenthesis union left parenthesis 2 comma infinity right parenthesis intersection left square bracket negative 1 comma infinity right parenthesis straight D subscript f plus g end subscript equals left square bracket negative 1 comma 2 right parenthesis union left parenthesis 2 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 open parentheses fraction numerator 2 x minus 6 over denominator 4 minus 2 x end fraction close parentheses times left parenthesis square root of x plus 1 end root right parenthesis left parenthesis f times g right parenthesis left parenthesis x right parenthesis equals fraction numerator x minus 3 left parenthesis square root of x plus 1 end root right parenthesis over denominator 2 minus x 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 2 right parenthesis union left parenthesis 2 comma infinity right parenthesis intersection left square bracket negative 1 comma infinity right parenthesis straight D subscript f times g end subscript equals left square bracket negative 1 comma 2 right parenthesis union left parenthesis 2 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 x minus 6 over denominator 4 minus 2 x end fraction right parenthesis divided by left parenthesis square root of x plus 1 end root right parenthesis open parentheses f over g close parentheses left parenthesis x right parenthesis equals fraction numerator x minus 3 over denominator left parenthesis 2 minus x right parenthesis left parenthesis square root of x plus 1 end root right parenthesis end fraction open parentheses f over g close parentheses left parenthesis x right parenthesis equals fraction numerator x minus 3 over denominator 2 square root of x plus 1 end root minus x square root of x plus 1 end root end fraction times fraction numerator 2 square root of x plus 1 end root minus x square root of x plus 1 end root over denominator 2 square root of x plus 1 end root plus x square root of x plus 1 end root end fraction open parentheses f over g close parentheses left parenthesis x right parenthesis equals fraction numerator left parenthesis x minus 3 right parenthesis left parenthesis 2 square root of x plus 1 end root minus x square root of x plus 1 end root right parenthesis over denominator left parenthesis 2 square root of x plus 1 end root right parenthesis squared minus left parenthesis x square root of x plus 1 end root right parenthesis squared end fraction open parentheses f over g close parentheses left parenthesis x right parenthesis equals fraction numerator left parenthesis x minus 3 right parenthesis left parenthesis 2 square root of x plus 1 end root minus x square root of x plus 1 end root right parenthesis over denominator 4 left parenthesis x plus 1 right parenthesis minus x squared left parenthesis x plus 1 right parenthesis end fraction open parentheses f over g close parentheses left parenthesis x right parenthesis equals fraction numerator left parenthesis x minus 3 right parenthesis left parenthesis 2 square root of x plus 1 end root minus x square root of x plus 1 end root right parenthesis over denominator left parenthesis x plus 1 right parenthesis left parenthesis 4 minus x squared right parenthesis end fraction straight D subscript f over g end subscript equals straight D subscript f intersection straight D subscript g minus left curly bracket x not equal to negative 1 comma x not equal to plus-or-minus 2 right curly bracket straight D subscript f over g end subscript equals left parenthesis negative infinity comma 2 right parenthesis union left parenthesis 2 comma infinity right parenthesis intersection left square bracket negative 1 comma infinity right parenthesis subscript g minus left curly bracket x not equal to negative 1 comma x not equal to plus-or-minus 2 right curly bracket space straight D subscript f over g end subscript equals left parenthesis negative 1 comma 2 right parenthesis union left parenthesis 2 comma infinity right parenthesis end style    

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

Tapi Roboguru masih mau belajar. Menurut kamu pembahasan kali ini sudah membantu, belum?

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