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 \geq 2

Find undefined (singularity) points:

x = 2

Combine real regions and undefined points for final function domain

x \leq - 2 or x > 2

π sin (2 x + 1)

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

f (x) = 10 - ln (x)

f (x) = \frac{x - 2}{8 x - 8}

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