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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.

 Mar 13, 2017

Best Answer 

 #2
avatar+884 
+7

Thank you so much CPhill.

 Mar 13, 2017
 #1
avatar+128794 
+8

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

 

 

cool cool cool

 Mar 13, 2017
 #2
avatar+884 
+7
Best Answer

Thank you so much CPhill.

ant101 Mar 13, 2017
 #3
avatar+128794 
+8

No prob......!!!!

 

 

cool cool cool

 Mar 13, 2017

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