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

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

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

domain

h (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

y = 4 + \frac{5}{1 + x - 3}

y = \frac{2}{x + 3}

f (x) = 5 (x^{2} - 20)

∣ x - 4 ∣

f (x) = - 5 lo g_{10} (x - 2)

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