What is the domain of f(x)=sqrt((24-2x-x^2)/(x^2-4)) ?

The domain of f(x)=sqrt((24-2x-x^2)/(x^2-4)) is -6<= x<-2\lor 2<x<= 4

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domain of f(x)=sqrt((24-2x-x^2)/(x^2-4))

domain

f (x) = \frac{24 - 2 x - x ^{2}}{x ^{2} - 4}

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

Interval Notation

[- 6, - 2) \cup (2, 4]

Solution steps

Find non-negative values for radicals:

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

Find undefined (singularity) points:

x = 2, x = - 2

Combine real regions and undefined points for final function domain

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

What is the domain of f(x)=sqrt((24-2x-x^2)/(x^2-4)) ?
The domain of f(x)=sqrt((24-2x-x^2)/(x^2-4)) is -6<= x<-2\lor 2<x<= 4