What is the domain of f(x)=sqrt((x^2+3x)/(x^2-16)) ?

The domain of f(x)=sqrt((x^2+3x)/(x^2-16)) is x 4

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domain of f(x)=sqrt((x^2+3x)/(x^2-16))

domain

f (x) = \frac{x ^{2} + 3 x}{x ^{2} - 16}

x < - 4 or - 3 \leq x \leq 0 or x > 4

Interval Notation

(- \infty, - 4) \cup [- 3, 0] \cup (4, \infty)

Solution steps

Find non-negative values for radicals:

x < - 4 or - 3 \leq x \leq 0 or x > 4

Find undefined (singularity) points:

x = 4, x = - 4

Combine real regions and undefined points for final function domain

x < - 4 or - 3 \leq x \leq 0 or x > 4

What is the domain of f(x)=sqrt((x^2+3x)/(x^2-16)) ?
The domain of f(x)=sqrt((x^2+3x)/(x^2-16)) is x<-4\lor-3<= x<= 0\lor x>4