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Find the domain of the real-valued function $$f(x)=\sqrt{-10x^2-11x+6}$$.Give the endpoints in your answer as common fractions, not mixed numbers or decimals.

ant101  Mar 13, 2017

#2
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Thank you so much CPhill.

ant101  Mar 13, 2017
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#1
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Note that the function value under the radical canot be less than zero

Set  this equal to 0

-10x^2 -11x + 6  = 0   multiply through by -1

10x^2 + 11x - 6  = 0   factor

(5x - 2)(2x + 3)  = 0    set each factor to 0   and we solve for x

This gives that x = 2/5  and x = -3/2

The answer comes from these two intervals (-inf, -3/2) U (2/5, inf)  or from the interval [-3/2, 2/5]

And in the original function, the domain of [-3/2, 2/5 ]  will make the quantity under the radical greater than or equal to 0

CPhill  Mar 13, 2017
#2
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Thank you so much CPhill.

ant101  Mar 13, 2017
#3
+75316
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No prob......!!!!

CPhill  Mar 13, 2017

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