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

#1**+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

CPhill
Mar 13, 2017