What is the domain of f(x,)=sqrt(((x^2-4))/(|x-2|)) ?

The domain of f(x,)=sqrt(((x^2-4))/(|x-2|)) is x 2

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domain of f(x,)=sqrt(((x^2-4))/(|x-2|))

domain

f (x,) = \frac{( x ^{2} - 4 )}{∣ x - 2 ∣}

x \leq - 2 or x > 2

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \leq - 2 or x > 2

Find undefined (singularity) points:

x = 2

Combine real regions and undefined points for final function domain

x \leq - 2 or x > 2

ln (- x^{2} + 1)

y = \frac{3}{5 + x}

f (x) = 2 ∣ x ∣ + 3 - x^{2}

x cos (2 x)

f (x) = - 5 x + 45

What is the domain of f(x,)=sqrt(((x^2-4))/(|x-2|)) ?
The domain of f(x,)=sqrt(((x^2-4))/(|x-2|)) is x<=-2\lor x>2