Question

What is the domain of the function: `f(x) =sqrt(( x- (3x^2)))`?

Answer 1

`D_f=[0,1/3]`

Explanation:

`x-3x^2>=0`
`3x^2-x<=0`
Lets solve the eq `3x^2-x=0`
`x(3x-1)=0`
`x=0 vv x=1/3`

Graph of `3x^2-x`:

graph{3x^2-x [-1.351, 1.35, -0.676, 0.675]}

So, `3x^2-x<=0` below the `x`-axis, or in the other words between zeros we have found:
`3x^2-x<=0 <=> x in [0,1/3]`

`D_f=[0,1/3]`