Mathematics
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Question

If f(x) is a polynomial function such that f left parenthesis x right parenthesis f open parentheses 1 over x close parentheses equals f left parenthesis x right parenthesis plus f open parentheses 1 over x close parentheses text  and  end text f left parenthesis 3 right parenthesis equals negative 80 then f(x)

  1. x to the power of 4 plus 1
  2. x to the power of 4 minus 1
  3. 1 minus x to the power of 4
  4. negative 1 minus x to the power of 4

The correct answer is: 1 minus x to the power of 4


    f left parenthesis x right parenthesis f open parentheses 1 over x close parentheses equals f left parenthesis x right parenthesis plus f open parentheses 1 over x close parentheses not stretchy rightwards double arrow f left parenthesis x right parenthesis equals plus-or-minus x to the power of n plus 1
f left parenthesis 3 right parenthesis equals negative 80 not stretchy rightwards double arrow f left parenthesis x right parenthesis equals negative x to the power of n plus 1 comma negative 3 to the power of n plus 1 equals negative 80 not stretchy rightwards double arrow n equals 4
therefore f left parenthesis x right parenthesis equals 1 minus x to the power of 4

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