What is the domain of f(x)=(sqrt(x-3))/(x-10) ?

The domain of f(x)=(sqrt(x-3))/(x-10) is 3 10

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domain of f(x)=(sqrt(x-3))/(x-10)

domain

f (x) = \frac{x - 3}{x - 10}

3 \leq x < 10 or x > 10

Interval Notation

[3, 10) \cup (10, \infty)

Solution steps

Find non-negative values for radicals:

x \geq 3

Find undefined (singularity) points:

x = 10

Combine real regions and undefined points for final function domain

3 \leq x < 10 or x > 10

f (x) = - 3

f (x) = \frac{1}{x - 7}

y = 4 - x^{2}

\frac{x - 5}{3 x + 2}

What is the domain of f(x)=(sqrt(x-3))/(x-10) ?
The domain of f(x)=(sqrt(x-3))/(x-10) is 3<= x<10\lor x>10