What is the domain of (sqrt(x^2-8))/(x-4) ?

The domain of (sqrt(x^2-8))/(x-4) is x 4

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domain of (sqrt(x^2-8))/(x-4)

domain

\frac{x ^{2} - 8}{x - 4}

x \leq - 22 or 22 \leq x < 4 or x > 4

Interval Notation

(- \infty, - 22] \cup [22, 4) \cup (4, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - 22 or x \geq 22

Find undefined (singularity) points:

x = 4

Combine real regions and undefined points for final function domain

x \leq - 22 or 22 \leq x < 4 or x > 4

f (x) = \frac{∣ 5 - x ∣}{x ^{2} - 12 x + 35}

y = \frac{6}{8 - x - 2}

\frac{x - 3}{ln ( 5 - x )}

\frac{5 ln ( x )}{x ^{3}}

What is the domain of (sqrt(x^2-8))/(x-4) ?
The domain of (sqrt(x^2-8))/(x-4) is x<=-2sqrt(2)\lor 2sqrt(2)<= x<4\lor x>4