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Question

Let f left parenthesis x right parenthesis equals fraction numerator open parentheses 2 x to the power of 3 end exponent minus 9 x to the power of 2 end exponent plus 12 x plus 3 close parentheses left parenthesis x minus a right parenthesis over denominator left parenthesis x minus a right parenthesis end fraction If range of f(x) is a proper subset of the set of real numbers, then the most exhaustive set in which a lies is

  1. left parenthesis negative ¥ comma 7 right parenthesis text end text text ㅌ end text text end text left parenthesis 8 comma ¥ right parenthesis    
  2. left parenthesis negative not equal to comma 7 right square bracket E left square bracket 8 comma ¥ right parenthesis    
  3. open parentheses negative infinity comma fraction numerator 1 over denominator 2 end fraction close square brackets union open square brackets fraction numerator 5 over denominator 2 end fraction comma infinity close parentheses    
  4. open parentheses negative infinity comma fraction numerator 1 over denominator 2 end fraction close parentheses union open parentheses fraction numerator 5 over denominator 2 end fraction comma infinity close parentheses    

The correct answer is: open parentheses negative infinity comma fraction numerator 1 over denominator 2 end fraction close parentheses union open parentheses fraction numerator 5 over denominator 2 end fraction comma infinity close parentheses



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