What is the domain of Y(x)=sqrt((1-|x|)/(2-|x|)) ?

The domain of Y(x)=sqrt((1-|x|)/(2-|x|)) is x 2

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domain of Y(x)=sqrt((1-|x|)/(2-|x|))

domain

Y (x) = \frac{1 - ∣ x ∣}{2 - ∣ x ∣}

x < - 2 or - 1 \leq x \leq 1 or x > 2

Interval Notation

(- \infty, - 2) \cup [- 1, 1] \cup (2, \infty)

Solution steps

Find non-negative values for radicals:

x < - 2 or - 1 \leq x \leq 1 or x > 2

Find undefined (singularity) points:

x = - 2, x = 2

Combine real regions and undefined points for final function domain

x < - 2 or - 1 \leq x \leq 1 or x > 2

2 x^{2} + 2 x - 1

f (x) = \frac{4 x - 1 - 2}{4 x - 1 + 5}

(x - 3)^{2}, x \geq 3

f (x) = {x + 1, x < 1}

f (x) = 4 - x^{2} + 1 - x^{2}

What is the domain of Y(x)=sqrt((1-|x|)/(2-|x|)) ?
The domain of Y(x)=sqrt((1-|x|)/(2-|x|)) is x<-2\lor-1<= x<= 1\lor x>2