What is the domain of f(x)=sqrt((|x|-2)/(2x+2)) ?

The domain of f(x)=sqrt((|x|-2)/(2x+2)) is -2 = 2

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domain of f(x)=sqrt((|x|-2)/(2x+2))

domain

f (x) = \frac{∣ x ∣ - 2}{2 x + 2}

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

Interval Notation

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

Solution steps

Find non-negative values for radicals:

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

Find undefined (singularity) points:

x = - 1

Combine real regions and undefined points for final function domain

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

f (x) = e^{x} - x

f (x) = lo g_{2} (x - 3)

f (x) = \frac{1}{x - 1}

(2 - x^{2}) \cdot (x^{2} - 9)

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