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

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

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

domain

f (x) = \frac{x}{x - 3}

x \leq 0 or x > 3

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \leq 0 or x > 3

Find undefined (singularity) points:

x = 3

Combine real regions and undefined points for final function domain

x \leq 0 or x > 3

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