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

Sep 16, 2015

${D}_{f} = \left[0 , \frac{1}{3}\right]$

#### Explanation:

$x - 3 {x}^{2} \ge 0$
$3 {x}^{2} - x \le 0$
Lets solve the eq $3 {x}^{2} - x = 0$
$x \left(3 x - 1\right) = 0$
$x = 0 \vee x = \frac{1}{3}$

Graph of $3 {x}^{2} - x$:

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

So, $3 {x}^{2} - x \le 0$ below the $x$-axis, or in the other words between zeros we have found:
$3 {x}^{2} - x \le 0 \iff x \in \left[0 , \frac{1}{3}\right]$

${D}_{f} = \left[0 , \frac{1}{3}\right]$