What is the domain of f(x)=sqrt((3x-6)/x) ?

The domain of f(x)=sqrt((3x-6)/x) is x = 2

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domain of f(x)=sqrt((3x-6)/x)

domain

f (x) = \frac{3 x - 6}{x}

x < 0 or x \geq 2

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x < 0 or x \geq 2

Find undefined (singularity) points:

x = 0

Combine real regions and undefined points for final function domain

x < 0 or x \geq 2

\frac{2}{x + 8}

5 \cdot 3^{x}

f (x) = - 2 x - 1

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

What is the domain of f(x)=sqrt((3x-6)/x) ?
The domain of f(x)=sqrt((3x-6)/x) is x<0\lor x>= 2