What is the domain of sqrt((x-4)/(x-2)) ?

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

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domain of sqrt((x-4)/(x-2))

domain

\frac{x - 4}{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

f (x) = \frac{x - 1}{x + 1}

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

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

\frac{2}{3 x - 1}

x^{2} (x + 1) (x - 3)

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