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

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

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

domain

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

- 5 \leq x < - 3 or x > 3

Interval Notation

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

Solution steps

Find non-negative values for radicals:

- 5 \leq 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

- 5 \leq x < - 3 or x > 3

f (x) = 2 x + 3, - 2 \leq x < 1

f (x) = x - 4 x^{3}

f (x) = \frac{( 4 x + 3 )}{( 2 x - 1 )}

f (x) = x^{2} + 4 x

f (x) = \frac{2 x - 7}{3}

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