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

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

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

domain

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

2 \leq x < 3 or x > 3

Interval Notation

[2, 3) \cup (3, \infty)

Solution steps

Find non-negative values for radicals:

x \geq 2

Find undefined (singularity) points:

x = 3

Combine real regions and undefined points for final function domain

2 \leq x < 3 or x > 3

f (x) = (x^{2} - 36)^{\frac{1}{3}}

f (x) = 460 x - 11040

f (x) = 4 x^{3} - 3 x^{4}

3 - x^{2}

y = 2 x - 6

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