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

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

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

domain

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

x < 3 or x \geq 6

Interval Notation

(- \infty, 3) \cup [6, \infty)

Solution steps

Find non-negative values for radicals:

x < 3 or x \geq 6

Find undefined (singularity) points:

x = 3

Combine real regions and undefined points for final function domain

x < 3 or x \geq 6

f (x) = \frac{x ^{2} - 49}{x ( x - 7 )}

f (x) = x^{2} + 8 x

y = 4 x - 3

sin (6 x), 0 \leq x \leq 2 π

(5, - 7), (8, 1)

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