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

\frac{1}{x ^{2} - x - 90}

lo g_{5} (3 x^{2} - 5 x + 2)

\frac{x ^{2} - 3}{x ^{2} - x - 2} + 1

f (x) = sin (x) + tan (x) + cot (x)

f (x) = 7 x^{2} - 12 x + 21

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