What is the domain of f(x)=(sqrt(x-5))/(x^2-64) ?

The domain of f(x)=(sqrt(x-5))/(x^2-64) is 5 8

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domain of f(x)=(sqrt(x-5))/(x^2-64)

domain

f (x) = \frac{x - 5}{x ^{2} - 64}

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, x = - 8

Combine real regions and undefined points for final function domain

5 \leq x < 8 or x > 8

arcsin (\frac{x - 8}{9}) + 5

\frac{4 - 9 x}{x ^{2} + 3 x - 40}

\frac{x - 2 + 2}{x ^{2} - 9}

2 - 3 x + 5 - x

f (x) = \frac{x}{x ^{2} - 81}

What is the domain of f(x)=(sqrt(x-5))/(x^2-64) ?
The domain of f(x)=(sqrt(x-5))/(x^2-64) is 5<= x<8\lor x>8