What is the domain of f(x)=sqrt((x^2-x-6)/(2-x^2)) ?

The domain of f(x)=sqrt((x^2-x-6)/(2-x^2)) is -2<= x<-sqrt(2)\lor sqrt(2)<x<= 3

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domain of f(x)=sqrt((x^2-x-6)/(2-x^2))

domain

f (x) = \frac{x ^{2} - x - 6}{2 - x ^{2}}

- 2 \leq x < - 2 or 2 < x \leq 3

Interval Notation

[- 2, - 2) \cup (2, 3]

Solution steps

Find non-negative values for radicals:

- 2 \leq x < - 2 or 2 < x \leq 3

Find undefined (singularity) points:

x = 2, x = - 2

Combine real regions and undefined points for final function domain

- 2 \leq x < - 2 or 2 < x \leq 3

What is the domain of f(x)=sqrt((x^2-x-6)/(2-x^2)) ?
The domain of f(x)=sqrt((x^2-x-6)/(2-x^2)) is -2<= x<-sqrt(2)\lor sqrt(2)<x<= 3