What is the domain of f(x)=sqrt((|x|-3)/(5-|x|)) ?

The domain of f(x)=sqrt((|x|-3)/(5-|x|)) is -5<x<=-3\lor 3<= x<5

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domain of f(x)=sqrt((|x|-3)/(5-|x|))

domain

f (x) = \frac{∣ x ∣ - 3}{5 - ∣ x ∣}

- 5 < x \leq - 3 or 3 \leq x < 5

Interval Notation

(- 5, - 3] \cup [3, 5)

Solution steps

Find non-negative values for radicals:

- 5 < x \leq - 3 or 3 \leq x < 5

Find undefined (singularity) points:

x = - 5, x = 5

Combine real regions and undefined points for final function domain

- 5 < x \leq - 3 or 3 \leq x < 5

What is the domain of f(x)=sqrt((|x|-3)/(5-|x|)) ?
The domain of f(x)=sqrt((|x|-3)/(5-|x|)) is -5<x<=-3\lor 3<= x<5