Answer
(0, 1)
Work Step by Step
The question asks for the domain of the function given in the problem
Given $f(x) = \frac {1}{\sqrt[4] {x - x^4}} > 0$
The domain is such that $x - x^4$ is greater than 0.
$x - x^4 > 0$
$x (1 - x^3) > 0$
$x (1 - x) (1 + x + x^2) \leq 0$
$x = 0, 1$
(-∞, 0) $\frac{(+)}{(-)(-)(+)} = (+)$
(0, 1) $\frac{(+)}{(+)(-)(+)} = (-)$
(1, ∞) $\frac{(+)}{(+)(+)(+)} = (+)$
Thus the Domain is (0, 1)