What is the domain of f(x)=(sqrt(x+4))/(x^2-4) ?

The domain of f(x)=(sqrt(x+4))/(x^2-4) is -4 2

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domain of f(x)=(sqrt(x+4))/(x^2-4)

domain

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

- 4 \leq x < - 2 or - 2 < x < 2 or x > 2

Interval Notation

[- 4, - 2) \cup (- 2, 2) \cup (2, \infty)

Solution steps

Find non-negative values for radicals:

x \geq - 4

Find undefined (singularity) points:

x = 2, x = - 2

Combine real regions and undefined points for final function domain

- 4 \leq x < - 2 or - 2 < x < 2 or x > 2

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

\frac{7 + 4 x}{6 - 5 x}

f (x) = x + 4

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

\frac{5 x}{x + 8} - 8

What is the domain of f(x)=(sqrt(x+4))/(x^2-4) ?
The domain of f(x)=(sqrt(x+4))/(x^2-4) is -4<= x<-2\lor-2<x<2\lor x>2