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Pertanyaan

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 straight f to the power of straight apostrophe open parentheses negative 1 close parentheses equals end style....

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

  2. undefined

  3. begin mathsize 14px style negative 15 over 2 end style 

  4. begin mathsize 14px style fraction numerator 15 over denominator 3 square root of 2 end fraction end style

  5. begin mathsize 14px style fraction numerator 15 over denominator 2 square root of 3 end fraction end style

R. RGFLSATU

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

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 :

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight u left parenthesis straight x right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 5 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight x end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell blank squared end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight v left parenthesis straight x right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of left parenthesis straight x squared plus 1 right parenthesis end root end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis x squared plus 1 right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell blank to the power of 1 half end exponent end cell end table end style   

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.

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