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

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

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

domain

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

x < 2 or x \geq 4

Interval Notation

(- \infty, 2) \cup [4, \infty)

Solution steps

Find non-negative values for radicals:

x < 2 or x \geq 4

Find undefined (singularity) points:

x = 2

Combine real regions and undefined points for final function domain

x < 2 or x \geq 4

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