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

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

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

domain

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

- 2 < x \leq 0 or x > 2

Interval Notation

(- 2, 0] \cup (2, \infty)

Solution steps

Find non-negative values for radicals:

- 2 < x \leq 0 or x > 2

Find undefined (singularity) points:

x = 2, x = - 2

Combine real regions and undefined points for final function domain

- 2 < x \leq 0 or x > 2

f (x) = x^{2} + 4 x + 1

\frac{7 x + 2}{x - 2}

f (x) = 6 x - 2

\frac{x ^{2} - 49}{x - 3}

What is the domain of f(x)=sqrt(x/(x^2-4)) ?
The domain of f(x)=sqrt(x/(x^2-4)) is -2<x<= 0\lor x>2