What is the domain of f(x)=(x-5)/((sqrt(x^2-9))) ?

The domain of f(x)=(x-5)/((sqrt(x^2-9))) is x 3

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domain of f(x)=(x-5)/((sqrt(x^2-9)))

domain

f (x) = \frac{x - 5}{( x ^{2} - 9 )}

x < - 3 or x > 3

Interval Notation

(- \infty, - 3) \cup (3, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - 3 or x \geq 3

Find undefined (singularity) points:

x = 3, x = - 3

Combine real regions and undefined points for final function domain

x < - 3 or x > 3

y, y \leq 3 x

f (x) = x^{2} - 13 = 13 - x^{2}

f (x) = lo g_{10} (3 x) 2 - x - 20

f (x) = - 3 2 x + 3 - 1

f (x) = \frac{4}{( x - 1 )} + 1

What is the domain of f(x)=(x-5)/((sqrt(x^2-9))) ?
The domain of f(x)=(x-5)/((sqrt(x^2-9))) is x<-3\lor x>3