What is the domain of f(x)=(sqrt(x-5))/(x-8) ?

The domain of f(x)=(sqrt(x-5))/(x-8) is 5 8

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domain of f(x)=(sqrt(x-5))/(x-8)

domain

f (x) = \frac{x - 5}{x - 8}

5 \leq x < 8 or x > 8

Interval Notation

[5, 8) \cup (8, \infty)

Solution steps

Find non-negative values for radicals:

x \geq 5

Find undefined (singularity) points:

x = 8

Combine real regions and undefined points for final function domain

5 \leq x < 8 or x > 8

What is the domain of f(x)=(sqrt(x-5))/(x-8) ?
The domain of f(x)=(sqrt(x-5))/(x-8) is 5<= x<8\lor x>8