Exercise
Determine the domain of the function:
y=\frac{1}{\sqrt[4]{4-x^2}}
Final Answer
Solution
Let’s find the domain of the function:
y=\frac{1}{\sqrt[4]{4-x^2}}
Because there is a denominator, the denominator must be different from zero:
\sqrt[4]{4-x^2}\neq 0
Also, there is a fourth root, so we need the expression inside the root to be non-negative:
4-x^2\geq 0
The two inequalities are equivalent to the inequality:
4-x^2>0
It is a square inequality. The roots of the quadratic equation:
4-x^2=0
are
x=\pm 2
Because we are looking for the section above the x-axis and the parabola “cries”, we get that the solution of the inequality is
-2<x<2
By absolute value definition, this inequality is equivalent to
|x|<2
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