Pertanyaan

Diberikan dua buah fungsi f ( x ) = 4 − 2 x 2 x − 6 dan g ( x ) = x + 1 . Tentukan rumus fungsi f + g , f ⋅ g , dan g f , serta selanjutnya tentukan domain dari fungsi yang baru terbentuk!

Diberikan dua buah fungsi $f (x) = \frac{2 x - 6}{4 - 2 x}$ dan $g (x) = x + 1$ .

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 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$

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