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Let p(x) = sqrt(-x), and q(x) = 8x^2 + 10x - 5.  What is the domain of p(q(x))?  Your answer will be of the form a <= x <= b.  Find b - a.

 Oct 14, 2020
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p(q) must be negative ( less than or = 0 ) for    sqrt(-x) to be a real number

    p(q) is a bolw shaped parabola

8x^2 + 10x -5   <= 0 

     From the quadratic formula the zeroes are -5/8 +- sqrt (65)/8  

              everything between the zeroes will be negative values

 

-5/8-sqrt(65)/8  <= x <= -5/8 + sqrt(65)/8

 
 Oct 14, 2020

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