What is the domain of f(x)=(sqrt(x-5))/(x-6) ?

The domain of f(x)=(sqrt(x-5))/(x-6) is 5 6

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domain of f(x)=(sqrt(x-5))/(x-6)

domain

f (x) = \frac{x - 5}{x - 6}

5 \leq x < 6 or x > 6

Interval Notation

[5, 6) \cup (6, \infty)

Solution steps

Find non-negative values for radicals:

x \geq 5

Find undefined (singularity) points:

x = 6

Combine real regions and undefined points for final function domain

5 \leq x < 6 or x > 6

(3, 6), (9, 8)

y = x^{3} + 2 x^{2} - 1

3 sin (\frac{1}{4} x - \frac{5}{3} π) - 3

f (x) = - (x - 1)^{3} + 2

f (x) = g (x) = - 3 (x + 6)

What is the domain of f(x)=(sqrt(x-5))/(x-6) ?
The domain of f(x)=(sqrt(x-5))/(x-6) is 5<= x<6\lor x>6