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

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

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

domain

2 - \frac{x}{x - 2}

x < 2 or x \geq 4

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) = (x - 2)^{2} (x + 1)^{3} (3 x - 8)

x^{2} - 1

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

y = \frac{1 - 6 x}{3}

(- 3, 0), (0, 4)

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