Answer
$(0,1) $
Work Step by Step
1. Express the inequality in the form $f(x)<0, f(x)>0, f(x)\leq 0$, or $f(x)\geq 0,$
where $f$ is a polynomial function.
$f(x)=\frac{1}{\sqrt {x-x^4}},$ Take the denominator and factorise.
$\sqrt {x-x^4} \gt 0,$
$x-x^4\gt 0,$
$x(1-x^3)\gt0,$
$x(1-x)(x^2+x+1)\gt0,$
2. The cut points are:
$(x)(1-x)(x^2+x+1)=0$
$x=0$ or $x=1$
3. Make a table or diagram: use the test values to make a table or diagram of the sign of each factor in each interval.
4. Test each interval's sign of $g(x)=x-x^4$ with a test value,
$\begin{array}{llll}
Intervals: & a=test.v. & factors,signs & g(a),signs \\
& &(a)(1-a)(a^2+a+1)& \\
(-\infty, 0) & -5 & (-)(+)(+)=(-) & Undefined\\
(0, 1) & \frac{1}{2} & (+)(+)(+)=(+) & (+)\\
(1,\infty) & 5 & (+)(-)(+)=(-) & Undefined
\end{array}$
5. Write the solution set, selecting the interval or intervals that satisfy the given inequality. If the inequality involves $\leq$ or $\geq$, include the boundary points.
The Domain is: $(0,1) $
