Pertanyaan

Diberikan dua buah fungsi f ( x ) = 2 x − 6 dan g ( x ) = 8 − 4 x . 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!

R. Diah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Pembahasan

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  

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Pertanyaan serupa

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

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