+129845 Simplify as
sqrt [ -3x^2 - x + 6 ]
The expression under the root must be ≥ 0 (we can't take the sq rt of a negative)
So
-3x^2 - x + 6 ≥ 0
This is a parabola that opens downward......all we have to do is to find the roots....the domain will lie between these roots an also include them....so...
-3x^2 - x + 6 = 0 multiply through by -1
3x^2 + x - 6 = 0
By the quadratic formula
x = [ -1 - sqrt [ 1^2 - 4*3* -6 ]/ [ 2 *3 ] = [ -1 - sqrt ( 73 ) ] / 6
and
x = [ -1 + sqrt (73) ] 6
So....the domain is
[ (-1 -sqrt 73) / 6 , (-1 + sqrt 73) / 6 ]
