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

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

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

domain

f (x) = \frac{( x ^{2} - 1 )}{∣ x - 2 ∣}

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

Interval Notation

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

Solution steps

Find non-negative values for radicals:

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

Find undefined (singularity) points:

x = 2

Combine real regions and undefined points for final function domain

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

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