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Jika diketahui fungsi f(x)=2x−7, g(x)=x2+5, dan (x)2x2−1. Maka (f∘g∘h−1)(x)=...

Pertanyaan

Jika diketahui fungsi f left parenthesis x right parenthesis equals 2 x minus 7 comma space g left parenthesis x right parenthesis equals x squared plus 5 comma space d a n space left parenthesis x right parenthesis 2 x squared minus 1. space M a k a space left parenthesis f ring operator g ring operator h to the power of negative 1 end exponent right parenthesis left parenthesis x right parenthesis=...

  1. x-6

  2. x+5

  3. x-5

  4. x+4

  5. x-4

A. Acfreelance

Master Teacher

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Pembahasan

Penyelesaian:

  • h left parenthesis x right parenthesis equals 2 x squared minus 1  y equals 2 x squared minus 1  y plus 1 equals 2 x squared  x equals square root of fraction numerator y plus 1 over denominator 2 end fraction end root  h to the power of negative 1 end exponent equals square root of fraction numerator x plus 1 over denominator 2 end fraction end root
  • f left parenthesis x right parenthesis equals 2 x minus 7 space d a n space g left parenthesis x right parenthesis equals x squared plus 5  left parenthesis f ring operator g ring operator h to the power of negative 1 end exponent right parenthesis left parenthesis x right parenthesis equals left parenthesis f ring operator left parenthesis g ring operator h to the power of negative 1 end exponent right parenthesis right parenthesis left parenthesis x right parenthesis  m i s a l equals left parenthesis g ring operator h to the power of negative 1 end exponent right parenthesis left parenthesis x right parenthesis equals p left parenthesis x right parenthesis  left parenthesis g ring operator h to the power of negative 1 end exponent right parenthesis left parenthesis x right parenthesis equals g open parentheses fraction numerator square root of x plus 1 end root over denominator 2 end fraction close parentheses  equals open parentheses square root of fraction numerator x plus 1 over denominator 2 end fraction end root close parentheses squared plus 5  equals fraction numerator x plus 1 over denominator 2 end fraction plus 5  equals fraction numerator x plus 1 over denominator 2 end fraction plus 10 over 2 equals fraction numerator x plus 11 over denominator 2 end fraction
  • left parenthesis f ring operator left parenthesis g ring operator h to the power of negative 1 end exponent right parenthesis right parenthesis left parenthesis x right parenthesis equals open parentheses f ring operator p close parentheses left parenthesis x right parenthesis  equals f open parentheses fraction numerator x plus 11 over denominator 2 end fraction close parentheses  equals 2 open parentheses fraction numerator x plus 11 over denominator 2 end fraction close parentheses minus 7  equals x plus 11 minus 7  equals x plus 4

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Jika f(x)=x+2, g(x)=x1​ dan h(x−1)=x−3. Tentukanlah (h∘g∘f)−1(x).

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