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

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

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

domain

f (x) = \frac{3 x}{x - 2}

x \leq 0 or x > 2

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \leq 0 or x > 2

Find undefined (singularity) points:

x = 2

Combine real regions and undefined points for final function domain

x \leq 0 or x > 2

f (x) = \frac{4 x ^{2} - 36}{x ^{2} - 2 x - 8}

f (x) = \frac{x ( x - 5 ) ^{2}}{x - 5}

f (x) = \frac{x - 4}{x ^{2} + 9}

f (x) = \frac{x ^{2}}{3}

\frac{2 x + 3}{3 x - 4}

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