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

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

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

domain

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

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

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \geq - 5

Find undefined (singularity) points:

x = 3, x = - 3

Combine real regions and undefined points for final function domain

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

y = x^{2} - 4 x

x sin (\frac{1}{x})

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

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

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

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