Answer
$(-∞, -2) U (-1, 1) U (2, ∞) $
Work Step by Step
Given $f(x) =\frac {1}{ \sqrt {x^4 - 5x^2 + 4}}$
In a even root function, the domain is defined such that the function is always at (if defined) or above 0, so $f(x) \geq 0$
$\frac {1}{ \sqrt {x^4 - 5x^2 + 4}} \geq 0$
$\frac {1}{x^4 - 5x^2 + 4} \geq 0$
$\frac {1}{(x^2 - 4)(x^2 - 1)} \geq 0$
$\frac {1}{(x+2)(x+1)(x-1)(x-2)}) \geq 0$
Find the zeros of the expression.
$x = -2, -1, 1, 2$
Test numbers in between those zero values to determine if the function is negative or positive
(-∞, -2) $\frac{(+)}{(-)(-)(-)(-)} = (+)$
(-2, -1) $\frac{(+)}{(+)(-)(-)(-)} = (-)$
(-1, 1) $\frac{(+)}{(+)(+)(-)(-)} = (+)$
(1, 2) $\frac{(+)}{(+)(+)(+)(-)} = (-)$
(2, ∞) $\frac{(+)}{(+)(+)(+)(+)} = (+)$
Thus the solution is $(-∞, -2) U (-1, 1) U (2, ∞) $