Pertanyaan

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!

Diberikan dua buah fungsi $(x) = \frac{2}{x - 3}$ dan $g (x) = 6 x + 5$ .

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 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$

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