+885 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.
+129852 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 ]
