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Pertanyaan

Tentukan rumus dari begin mathsize 14px style f plus g end style, begin mathsize 14px style f minus g end style, begin mathsize 14px style g minus f end style dan begin mathsize 14px style f cross times g end style untuk begin mathsize 14px style f end style dan begin mathsize 14px style g end style pada begin mathsize 14px style R end style dengan ketentuan sebagai berikut:

b. begin mathsize 14px style f left parenthesis x right parenthesis equals fraction numerator 1 over denominator x plus 1 end fraction end style, untuk begin mathsize 14px style x not equal to negative 1 end style dan begin mathsize 14px style left parenthesis x right parenthesis equals fraction numerator 5 x over denominator 2 x minus 4 end fraction end style, untuk begin mathsize 14px style x not equal to 2 end style 

N. Indah

Master Teacher

Mahasiswa/Alumni Universitas Diponegoro

Jawaban terverifikasi

Jawaban

diperoleh rumusnya adalah left parenthesis f plus g right parenthesis left parenthesis x right parenthesis equals fraction numerator 5 x squared plus 7 x minus 4 over denominator 2 x squared minus 2 x minus 4 end fractionleft parenthesis f minus g right parenthesis left parenthesis x right parenthesis equals fraction numerator negative 5 x squared minus 3 x minus 4 over denominator 2 x squared minus 2 x minus 4 end fractionleft parenthesis g minus f right parenthesis left parenthesis x right parenthesis equals fraction numerator 5 x squared plus 3 x plus 4 over denominator 2 x squared minus 2 x minus 4 end fraction, dan left parenthesis f cross times g right parenthesis left parenthesis x right parenthesis equals fraction numerator 5 x over denominator 2 x squared minus 4 x plus 2 x minus 4 end fraction.

Pembahasan

Diketahui  begin mathsize 14px style f left parenthesis x right parenthesis equals fraction numerator 1 over denominator x plus 1 end fraction end style, untuk begin mathsize 14px style x not equal to negative 1 end style dan g left parenthesis x right parenthesis equals fraction numerator 5 x over denominator 2 x minus 4 end fraction, untuk begin mathsize 14px style x not equal to 2 end style, maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis f plus g right parenthesis left parenthesis x right parenthesis end cell equals cell f left parenthesis x right parenthesis plus g left parenthesis x right parenthesis end cell row blank equals cell open parentheses fraction numerator 1 over denominator x plus 1 end fraction close parentheses plus open parentheses fraction numerator 5 x over denominator left parenthesis 2 x minus 4 end fraction close parentheses end cell row blank equals cell fraction numerator left parenthesis 2 x minus 4 right parenthesis plus 5 x left parenthesis x plus 1 right parenthesis over denominator open parentheses x plus 1 close parentheses left parenthesis 2 x minus 4 right parenthesis end fraction end cell row blank equals cell fraction numerator 2 x minus 4 plus 5 x squared plus 5 x over denominator 2 x squared minus 4 x plus 2 x minus 4 end fraction end cell row blank equals cell fraction numerator 5 x squared plus 7 x minus 4 over denominator 2 x squared minus 2 x minus 4 end fraction comma space untuk space x not equal to negative 1 space atau space x not equal to 2 end cell row blank blank blank row cell left parenthesis f minus g right parenthesis left parenthesis x right parenthesis end cell equals cell f left parenthesis x right parenthesis minus g left parenthesis x right parenthesis end cell row blank equals cell open parentheses fraction numerator 1 over denominator x plus 1 end fraction close parentheses minus open parentheses fraction numerator 5 x over denominator left parenthesis 2 x minus 4 end fraction close parentheses end cell row blank equals cell fraction numerator left parenthesis 2 x minus 4 right parenthesis minus 5 x left parenthesis x plus 1 right parenthesis over denominator left parenthesis x plus 1 right parenthesis left parenthesis 2 x minus 4 right parenthesis end fraction end cell row blank equals cell fraction numerator 2 x minus 4 minus 5 x squared minus 5 x over denominator 2 x squared minus 4 x plus 2 x minus 4 end fraction end cell row blank equals cell fraction numerator negative 5 x squared minus 3 x minus 4 over denominator 2 x squared minus 2 x minus 4 end fraction comma space untuk space x not equal to negative 1 space straight a straight t straight a straight u space x not equal to 2 end cell row blank blank blank row cell left parenthesis g minus f right parenthesis left parenthesis x right parenthesis end cell equals cell g left parenthesis x right parenthesis minus f left parenthesis x right parenthesis end cell row blank equals cell open parentheses fraction numerator 5 x over denominator left parenthesis 2 x minus 4 end fraction close parentheses minus open parentheses fraction numerator 1 over denominator x plus 1 end fraction close parentheses end cell row blank equals cell fraction numerator 5 x left parenthesis x plus 1 right parenthesis minus left parenthesis 2 x minus 4 right parenthesis over denominator left parenthesis x plus 1 right parenthesis left parenthesis 2 x minus 4 right parenthesis end fraction end cell row blank equals cell fraction numerator 5 x squared plus 5 x minus 2 x plus 4 over denominator 2 x squared minus 4 x plus 2 x minus 4 end fraction end cell row blank equals cell fraction numerator 5 x squared plus 3 x plus 4 over denominator 2 x squared minus 2 x minus 4 end fraction comma space untuk space x not equal to negative 1 space a t a u space x not equal to 2 end cell row blank blank blank row cell left parenthesis f cross times g right parenthesis left parenthesis x right parenthesis end cell equals cell f left parenthesis x right parenthesis cross times g left parenthesis x right parenthesis end cell row blank equals cell open parentheses fraction numerator 1 over denominator x plus 1 end fraction close parentheses cross times open parentheses fraction numerator 5 x over denominator left parenthesis 2 x minus 4 end fraction close parentheses end cell row blank equals cell fraction numerator 5 x over denominator left parenthesis x plus 1 right parenthesis left parenthesis 2 x minus 4 right parenthesis end fraction end cell row blank equals cell fraction numerator 5 x over denominator 2 x squared minus 4 x plus 2 x minus 4 end fraction comma space untuk space x not equal to negative 1 space atau space x not equal to 2 end cell row blank blank blank end table end style 

Dengan demikian, diperoleh rumusnya adalah left parenthesis f plus g right parenthesis left parenthesis x right parenthesis equals fraction numerator 5 x squared plus 7 x minus 4 over denominator 2 x squared minus 2 x minus 4 end fractionleft parenthesis f minus g right parenthesis left parenthesis x right parenthesis equals fraction numerator negative 5 x squared minus 3 x minus 4 over denominator 2 x squared minus 2 x minus 4 end fractionleft parenthesis g minus f right parenthesis left parenthesis x right parenthesis equals fraction numerator 5 x squared plus 3 x plus 4 over denominator 2 x squared minus 2 x minus 4 end fraction, dan left parenthesis f cross times g right parenthesis left parenthesis x right parenthesis equals fraction numerator 5 x over denominator 2 x squared minus 4 x plus 2 x minus 4 end fraction.

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