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

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Answer 1 · 2015-09-16T11:06:16

$D_f=[0,1/3]$

$x-3x^2>=0$
$3x^2-x<=0$
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:
$3x^2-x<=0 <=> x in [0,1/3]$

$D_f=[0,1/3]$

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