+0  
 
0
94
3
avatar+230 

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

Best Answer 

 #2
avatar+230 
+5

Thank you so much CPhill.

ant101  Mar 13, 2017
Sort: 

3+0 Answers

 #1
avatar+76929 
+5

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

CPhill  Mar 13, 2017
 #2
avatar+230 
+5
Best Answer

Thank you so much CPhill.

ant101  Mar 13, 2017
 #3
avatar+76929 
+5

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

 

 

cool cool cool

CPhill  Mar 13, 2017

7 Online Users

avatar
avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details