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

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

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

domain

f (x) = \frac{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{( 2 x ^{(2)} - 4 )}{( x - 1 )})

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

\frac{x}{x ^{2} + 5 x - 6}

f (x) = 2 x + 1, x < 0

y = \frac{1}{4} csc (4) (x - \frac{5 π}{6}) + 7

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