What is the domain of f(x)=sqrt((x^2-16)/x) ?

The domain of f(x)=sqrt((x^2-16)/x) is -4 = 4

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domain of f(x)=sqrt((x^2-16)/x)

domain

f (x) = \frac{x ^{2} - 16}{x}

- 4 \leq x < 0 or x \geq 4

Interval Notation

[- 4, 0) \cup [4, \infty)

Solution steps

Find non-negative values for radicals:

- 4 \leq x < 0 or x \geq 4

Find undefined (singularity) points:

x = 0

Combine real regions and undefined points for final function domain

- 4 \leq x < 0 or x \geq 4

What is the domain of f(x)=sqrt((x^2-16)/x) ?
The domain of f(x)=sqrt((x^2-16)/x) is -4<= x<0\lor x>= 4