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Pertanyaan

Diberikan dua buah fungsi f ( x ) = x ​ dan g ( x ) = x 2 + 1 . Tentukan rumus fungsi f + g , f ⋅ g , dan g f ​ , serta selanjutnya tentukan domain dari fungsi yang baru terbentuk!

Diberikan dua buah fungsi  dan .

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

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R. Diah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

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Pembahasan

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  

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Diberikan dua buah fungsi ( x ) = x − 3 2 ​ dan g ( x ) = 6 x + 5 . Tentukan rumus fungsi f + g , f ⋅ g , dan g f ​ , serta selanjutnya tentukan domain dari fungsi yang baru terbentuk!

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