What is the domain of 1/(sqrt(x-5)) ?

The domain of 1/(sqrt(x-5)) is x>5

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domain of 1/(sqrt(x-5))

domain

\frac{1}{x - 5}

x > 5

Interval Notation

(5, \infty)

Solution steps

Find non-negative values for radicals:

x \geq 5

Find undefined (singularity) points:

x = 5

Combine real regions and undefined points for final function domain

x > 5

(- 8, 12), (- 13, - 2)

f (x) = \frac{x + 6}{x - 4}

\frac{1}{x - 1}

f (x) = \frac{2 x + 1}{x ^{2} - x - 6}

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