Jika  maka nilai k yang tepat adalah ….

Pertanyaan

Jika begin mathsize 14px style open parentheses x close parentheses equals fraction numerator 1 over denominator square root of x squared minus sign 2 end root end fraction comma space open parentheses fog close parentheses open parentheses x close parentheses equals fraction numerator 1 over denominator square root of x squared plus 6 x plus 7 end root end fraction space dan space g open parentheses x and k close parentheses equals x plus 5 end style maka nilai k yang tepat adalah ….

  1. 2

  2. -2

  3. -4

  4. -6

  5. 5

M. Robo

Master Teacher

Jawaban terverifikasi

Pembahasan

begin mathsize 14px style blank end stylebegin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis fog right parenthesis left parenthesis straight x right parenthesis end cell equals cell fraction numerator 1 over denominator square root of straight x squared plus 6 straight x plus 7 end root end fraction end cell row cell straight f left parenthesis straight g left parenthesis straight x right parenthesis right parenthesis end cell equals cell fraction numerator 1 over denominator square root of straight x squared plus 6 straight x plus 7 end root end fraction end cell row cell fraction numerator 1 over denominator square root of straight g left parenthesis straight x right parenthesis squared minus 2 end root end fraction end cell equals cell fraction numerator 1 over denominator square root of straight x squared plus 6 straight x plus 7 end root end fraction end cell row cell straight g left parenthesis straight x right parenthesis squared minus 2 end cell equals cell straight x squared plus 6 straight x plus 7 end cell row cell straight g left parenthesis straight x right parenthesis end cell equals cell square root of straight x squared plus 6 straight x plus 9 end root end cell end table end style   


Karena begin mathsize 14px style g open parentheses x and k close parentheses equals x plus 5 end style maka:

undefinedbegin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight g left parenthesis straight x plus straight k right parenthesis end cell equals cell square root of left parenthesis straight x plus straight k right parenthesis squared plus 6 left parenthesis straight x plus straight k right parenthesis plus 9 end root end cell row cell straight x plus 5 end cell equals cell square root of straight x squared plus 2 kx plus straight k squared plus 6 straight x plus 6 straight k plus 9 end root end cell row cell left parenthesis straight x plus 5 right parenthesis squared end cell equals cell straight x to the power of 2 end exponent plus left parenthesis 2 straight k plus 6 right parenthesis straight x plus left parenthesis straight k squared plus 6 straight k plus 9 right parenthesis end cell row cell straight x squared plus 10 straight x plus 25 end cell equals cell straight x squared plus left parenthesis 2 straight k plus 6 right parenthesis straight x plus left parenthesis straight k squared plus 6 straight k plus 9 right parenthesis end cell end table end style    

Ambil salah satu persamaan :

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 10 straight x end cell equals cell left parenthesis 2 straight k plus 6 right parenthesis straight x end cell row 10 equals cell 2 straight k plus 6 end cell row 4 equals cell 2 straight k end cell row 2 equals straight k end table end style   

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Garis ( k - 2)y = 3x berpotongan dengan kurva xy = 1 - x di dua titik. Nilai k yang tepat adalah ….

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