What is the domain of f(x)=(sqrt(x^2-4))/(x^2-2x+1) ?

The domain of f(x)=(sqrt(x^2-4))/(x^2-2x+1) is x = 2

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domain of f(x)=(sqrt(x^2-4))/(x^2-2x+1)

domain

x \leq - 2 or x \geq 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 = 1

Combine real regions and undefined points for final function domain

x \leq - 2 or x \geq 2

What is the domain of f(x)=(sqrt(x^2-4))/(x^2-2x+1) ?
The domain of f(x)=(sqrt(x^2-4))/(x^2-2x+1) is x<=-2\lor x>= 2