What is the domain of f(x)=(sqrt(x^2-2x))/(x-3) ?

The domain of f(x)=(sqrt(x^2-2x))/(x-3) is x 3

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domain of f(x)=(sqrt(x^2-2x))/(x-3)

domain

x \leq 0 or 2 \leq x < 3 or x > 3

Interval Notation

(- \infty, 0] \cup [2, 3) \cup (3, \infty)

Solution steps

Find non-negative values for radicals:

x \leq 0 or x \geq 2

Find undefined (singularity) points:

x = 3

Combine real regions and undefined points for final function domain

x \leq 0 or 2 \leq x < 3 or x > 3

What is the domain of f(x)=(sqrt(x^2-2x))/(x-3) ?
The domain of f(x)=(sqrt(x^2-2x))/(x-3) is x<= 0\lor 2<= x<3\lor x>3