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Let f(x) = (3x^2 - 10x - 25)/(x + 4) and g(x) = (3x^2 - 10x - 25)/(3x^2 + 12x + 10). Find the sum of all real numbers that are not in the domain of f(g(x)).

 Oct 26, 2020
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First ....no x values that cause the denominator of g(x) = 0 would be allowed

    -2 +- sqrt(6)/3   not allowed

then any value of g(x) that causes denominator to f(x) = 0 is not allowed

   this woud be when g(x) = -4

      3x^2-10x-25 / (3x^2+12x+10) = - 4

       3x^2-10x-25 = -12x^2-48x-40

   15x^2 +38x+15 = 0 

       results in -19/15 +-2 sqrt(34)/15     not allowed

 

 

Summed = -2 + -2 + -19/15 + -19/15 = .................

 Oct 26, 2020

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