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Pertanyaan

Diketahui begin mathsize 14px style f left parenthesis x right parenthesis equals negative fraction numerator 4 over denominator square root of x plus 2 end root end fraction plus 2 x space dan space g left parenthesis x right parenthesis equals 2 over x end style. Rumus fungsi begin mathsize 14px style f over g left parenthesis x right parenthesis end style adalah ....

  1. begin mathsize 14px style negative fraction numerator 2 x over denominator square root of x plus 2 end root end fraction plus 2 x squared end style   

  2. begin mathsize 14px style negative fraction numerator 4 x over denominator square root of x plus 2 end root end fraction plus x squared end style  

  3. begin mathsize 14px style negative fraction numerator 2 x over denominator square root of x plus 2 end root end fraction plus x squared end style  

  4. begin mathsize 14px style negative fraction numerator 4 x over denominator square root of x plus 2 end root end fraction plus 2 x squared end style  

  5. begin mathsize 14px style negative fraction numerator 2 over denominator square root of x plus 2 end root end fraction plus x end style  

Y. Dwi

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

Ingat bahwa begin mathsize 14px style f over g left parenthesis x right parenthesis equals fraction numerator f left parenthesis x right parenthesis over denominator g left parenthesis x right parenthesis space end fraction end style. Akibatnya, diperoleh hasil sebagai berikut.    

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator f over denominator g space end fraction left parenthesis x right parenthesis end cell equals cell fraction numerator negative begin display style fraction numerator 4 over denominator square root of x plus 2 end root end fraction end style plus 2 x over denominator begin display style 2 over x end style end fraction end cell row blank equals cell fraction numerator negative begin display style fraction numerator 4 over denominator square root of x plus 2 end root end fraction end style plus 2 x over denominator begin display style 2 over x end style end fraction times x over x end cell row blank equals cell fraction numerator open parentheses negative begin display style fraction numerator 4 over denominator square root of x plus 2 end root end fraction end style plus 2 x close parentheses x over denominator begin display style 2 end style end fraction end cell row blank equals cell fraction numerator negative begin display style fraction numerator 4 x over denominator square root of x plus 2 end root end fraction end style plus 2 x squared over denominator begin display style 2 end style end fraction end cell row blank equals cell 1 half open parentheses negative fraction numerator 4 x over denominator square root of x plus 2 end root end fraction plus 2 x squared close parentheses end cell row blank equals cell negative fraction numerator 2 x over denominator square root of x plus 2 end root end fraction plus x squared end cell end table 

Jadi, jawaban yang tepat adalah C.

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