What is the domain of f(x)=(sqrt(x-5))/(x-11) ?

The domain of f(x)=(sqrt(x-5))/(x-11) is 5 11

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domain of f(x)=(sqrt(x-5))/(x-11)

domain

f (x) = \frac{x - 5}{x - 11}

5 \leq x < 11 or x > 11

Interval Notation

[5, 11) \cup (11, \infty)

Solution steps

Find non-negative values for radicals:

x \geq 5

Find undefined (singularity) points:

x = 11

Combine real regions and undefined points for final function domain

5 \leq x < 11 or x > 11

f (x) = 1 - \frac{1}{5} x

f (x) = \frac{3 x ^{5}}{2 x ^{3} + x}

- \frac{1}{2 x ^{\frac{3}{2}}}

f (x) = - 4 x^{2} + 48 x

x^{2} - 4

What is the domain of f(x)=(sqrt(x-5))/(x-11) ?
The domain of f(x)=(sqrt(x-5))/(x-11) is 5<= x<11\lor x>11