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Jika , maka nilai f(- 5) adalah...

Jika begin mathsize 12px style f to the power of negative 1 end exponent open parentheses x minus 1 close parentheses equals fraction numerator 4 minus 3 x over denominator x minus 2 end fraction end style, maka nilai f(- 5) adalah...

  1. begin mathsize 12px style negative 8 over 3 end style

  2. - 2

  3. 0

  4. 2

  5. 4

Jawaban:

Perhatikan sifat fungsi invers

Jika begin mathsize 12px style f open parentheses x close parentheses equals fraction numerator a x plus b over denominator c x plus d end fraction end style, maka size 12px f to the power of size 12px minus size 12px 1 end exponent open parentheses size 12px x close parentheses size 12px equals fraction numerator size 12px minus size 12px d size 12px x size 12px plus size 12px b over denominator size 12px c size 12px x size 12px minus size 12px a end fraction. Invers adalah fungsi kebalikan dari komposisi suatu fungsi.

Perhatikan soalnya

Jika begin mathsize 12px style f to the power of negative 1 end exponent open parentheses x minus 1 close parentheses equals fraction numerator 4 minus 3 x over denominator x minus 2 end fraction end style, nilai x ditambahkan 1 (untuk mendapatkan begin mathsize 12px style f to the power of negative 1 end exponent open parentheses x close parentheses end style)

Maka

 begin mathsize 12px style f to the power of negative 1 end exponent open parentheses x minus 1 plus 1 close parentheses equals fraction numerator 4 minus 3 open parentheses x plus 1 close parentheses over denominator open parentheses x plus 1 close parentheses minus 2 end fraction  f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator negative 3 x plus 1 over denominator x minus 1 end fraction end style

Karena jika begin mathsize 12px style f open parentheses x close parentheses equals fraction numerator a x plus b over denominator c x plus d end fraction end style, maka size 12px f to the power of size 12px minus size 12px 1 end exponent open parentheses size 12px x close parentheses size 12px equals fraction numerator size 12px minus size 12px d size 12px x size 12px plus size 12px b over denominator size 12px c size 12px x size 12px minus size 12px a end fraction.

Maka:

begin mathsize 12px style f open parentheses x close parentheses equals fraction numerator x plus 1 over denominator x plus 3 end fraction comma space m a s u k k a n space x equals negative 5  f open parentheses negative 5 close parentheses equals fraction numerator negative 5 plus 1 over denominator negative 5 plus 3 end fraction  f open parentheses negative 5 close parentheses equals 2 end style

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