Pertanyaan

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!

Diberikan dua buah fungsi $f (x) = \frac{1}{x - 1}$ dan $g (x) = \frac{x}{2 x - 1}$ .

Tentukan rumus fungsi $f + g$ , $f \cdot g$ , dan $\frac{f}{g}$ , 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 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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