SOLUTION: what is the domain of the following function f(x) = sqrt(((x^3)/3) - x) a)(−infinite, -sqrt3]and[0, infinite) b)[−sqrt3, 0]and[sqrt3, infinite) c)[−

Algebra ->  Functions -> SOLUTION: what is the domain of the following function f(x) = sqrt(((x^3)/3) - x) a)(−infinite, -sqrt3]and[0, infinite) b)[−sqrt3, 0]and[sqrt3, infinite) c)[−      Log On


   



Question 901641: what is the domain of the following function
f(x) = sqrt(((x^3)/3) - x)
a)(−infinite, -sqrt3]and[0, infinite)
b)[−sqrt3, 0]and[sqrt3, infinite)
c)[−sqrt3, sqrt3]
d)(−infinite, −sqrt3]and[sqrt3, infinite)

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The argument of the square root must be non-negative:
graph%28300%2C300%2C-4%2C4%2C-4%2C4%2Cx%5E3%2F3-x%29
x%5E3%2F3-x%3E=0
x%28x%5E2%2F3-1%29%3E=0
Critical points:
x%5E2%2F3-1=0
x%5E2=3
x=0+%2B-+sqrt%283%29
and
x=0
So from the graph, it looks like, the regions where the function is non-negative are,
(-sqrt%283%29,0)U(sqrt%283%29,infinity)