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Fungsi didefinisikan dengan . Invers fungsi f(x) adalah ....

Fungsi f colon straight R rightwards arrow straight R didefinisikan dengan straight f left parenthesis straight x right parenthesis equals fraction numerator 2 straight x minus 1 over denominator 3 straight x plus 4 end fraction comma straight x not equal to fraction numerator negative 4 over denominator 3 end fraction . Invers fungsi f(x) adalah ....

  1. straight f to the power of 1 left parenthesis straight x right parenthesis equals fraction numerator 4 straight x minus 1 over denominator 3 straight x plus 2 end fraction comma straight x not equal to fraction numerator negative 2 over denominator 3 end fraction

  2. straight f to the power of 1 left parenthesis straight x right parenthesis equals fraction numerator straight x plus 1 over denominator 3 straight x minus 2 end fraction comma straight x not equal to 2 over 3

  3. straight f to the power of 1 left parenthesis straight x right parenthesis equals fraction numerator 4 straight x plus 1 over denominator 2 minus 3 straight x end fraction comma straight x not equal to 2 over 3

  4. straight f to the power of 1 left parenthesis straight x right parenthesis equals fraction numerator 4 straight x minus 1 over denominator 3 straight x minus 2 end fraction comma straight x not equal to 2 over 3

  5. straight f to the power of 1 left parenthesis straight x right parenthesis equals fraction numerator 4 straight x plus 1 over denominator 3 straight x plus 4 end fraction comma straight x not equal to fraction numerator negative 4 over denominator 3 end fraction

Jawaban:

Jika f left parenthesis x right parenthesis equals fraction numerator a x plus b over denominator c x plus d end fraction rightwards arrow f to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator negative d x plus b over denominator c x minus a end fraction

f to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator negative 4 x minus 1 over denominator 3 x minus 2 end fraction equals fraction numerator negative left parenthesis 4 x plus 1 right parenthesis over denominator negative left parenthesis 2 minus 3 x right parenthesis end fraction equals fraction numerator 4 x plus 1 over denominator 2 minus 3 x end fraction

atau

Misal f(x) = y, maka

y equals fraction numerator 2 straight x minus 1 over denominator 3 straight x plus 4 end fraction  3 x y plus 4 y equals 2 x minus 1  3 x y minus 2 x equals negative 4 y minus 1  x left parenthesis 3 y minus 2 right parenthesis equals negative left parenthesis 4 y plus 1 right parenthesis  x equals negative fraction numerator 4 y plus 1 over denominator 3 y minus 2 end fraction  x equals fraction numerator 4 y plus 1 over denominator 2 minus 3 y end fraction  S e h i n g g a space i n v e r s space f u n g s i space f to the power of negative 1 end exponent left parenthesis x right parenthesis comma  f to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator 4 x plus 1 over denominator 2 minus 3 x end fraction comma x not equal to 2 over 3

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