+0  
 
0
45
3
avatar+742 

Can someone check my work/ I'm keep on getting \(\left[-\frac{3}{2},\:\frac{2}{5}\right]\) as my answer. 

 

Question: 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  Nov 28, 2018
 #1
avatar+92814 
+2

We need to have  [ since the result inside the radical can't be negative ]

 

-10x^2 - 11x + 6  ≥  0     (1)     multiply both sides by  -1,  reverse the inequality sign

 

10x^2 + 11x - 6 ≤ 0      set to 0 and factor

 

10x^2 + 11x - 6  =  0

 

(5x -2) ( 2x + 3) = 0

 

Set each factor to 0 and solve for x

 

x =  2/5        or    x = -3/2

 

The intervals that make (1)  true come from either

 

( -inf, -3/2)    or    [ -3/2, 2/5]     or  (2/5, inf)

 

Test a point in the middle interval   - I'll pick 0 -  and test it in (1)

If  0, makes it true, then this is the correct interval....so...

 

-10(0)^2  - 11(0)+ 6  ≥  0        is true

 

So...you are correct Ant !!!.....the answer is    [ -3/2, 2/5 ]

 

 

cool cool cool

CPhill  Nov 28, 2018
edited by CPhill  Nov 29, 2018
 #2
avatar+742 
+2

Thank you, CPhill! I understand better now!

ant101  Nov 29, 2018
 #3
avatar+92814 
0

Thanks, Ant !!!

 

cool cool cool

CPhill  Nov 29, 2018

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