Pertanyaan

Jika diberikan maka nilai dari ....

Jika diberikan $begin mathsize 14px style straight f open parentheses straight x close parentheses equals fraction numerator 5 straight x squared over denominator square root of straight x squared plus 1 end root end fraction blank end style$ maka nilai dari ....

$begin mathsize 14px style negative fraction numerator 5 over denominator square root of 2 end fraction end style$
$- \frac{5}{2}$
$begin mathsize 14px style fraction numerator 15 over denominator 3 square root of 2 end fraction end style$
$begin mathsize 14px style fraction numerator 15 over denominator 2 square root of 3 end fraction end style$

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

Misalkan : Maka diperoleh, Sehingga, Jadi, Dengan demikian, jawaban yang tepat adalah C.

$begin mathsize 14px style straight f open parentheses straight x close parentheses equals fraction numerator 5 straight x squared over denominator square root of straight x squared plus 1 end root end fraction end style$

Misalkan :

Maka diperoleh,

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight u to the power of apostrophe left parenthesis straight x right parenthesis end cell equals cell 10 straight x end cell row blank blank blank row cell straight v to the power of apostrophe left parenthesis straight x right parenthesis end cell equals cell 1 half left parenthesis x squared plus 1 right parenthesis to the power of 1 half minus 1 end exponent times left parenthesis 2 x right parenthesis end cell row blank equals cell fraction numerator 2 x left parenthesis x squared plus 1 right parenthesis to the power of negative begin display style 1 half end style end exponent over denominator 2 end fraction end cell row blank equals cell fraction numerator straight x over denominator square root of left parenthesis straight x squared plus 1 right parenthesis end root end fraction end cell end table end style$

Sehingga,

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight f to the power of straight apostrophe left parenthesis straight x right parenthesis end cell equals cell fraction numerator straight u to the power of straight apostrophe left parenthesis straight x right parenthesis blank straight v left parenthesis straight x right parenthesis minus straight u left parenthesis straight x right parenthesis blank straight v to the power of straight apostrophe left parenthesis straight x right parenthesis over denominator blank end fraction end cell row cell straight f to the power of straight apostrophe left parenthesis straight x right parenthesis end cell equals cell fraction numerator left parenthesis 10 straight x right parenthesis left parenthesis square root of straight x squared plus 1 end root right parenthesis minus left parenthesis 5 straight x squared right parenthesis left parenthesis fraction numerator straight x over denominator square root of straight x squared plus 1 end root end fraction right parenthesis over denominator blank end fraction blank end cell row cell straight f to the power of straight apostrophe left parenthesis straight x right parenthesis end cell equals cell fraction numerator 10 straight x left parenthesis straight x squared plus 1 right parenthesis minus 5 straight x cubed over denominator straight x squared plus 1 end fraction end cell row cell straight f to the power of straight apostrophe left parenthesis straight x right parenthesis end cell equals cell fraction numerator 10 straight x cubed plus 10 straight x minus 5 straight x cubed over denominator straight x squared plus 1 end fraction end cell row cell straight f to the power of straight apostrophe left parenthesis straight x right parenthesis end cell equals cell fraction numerator 5 straight x cubed plus 10 straight x over denominator straight x squared plus 1 end fraction end cell end table end style$

Jadi,

$begin mathsize 14px style straight f to the power of straight apostrophe left parenthesis 1 right parenthesis equals fraction numerator 5 left parenthesis negative 1 right parenthesis cubed plus 10 left parenthesis negative 1 right parenthesis over denominator left parenthesis negative 1 right parenthesis squared plus 1 end fraction equals negative 15 over 2 end style$

Dengan demikian, jawaban yang tepat adalah C.