What is the domain of f(x)=sqrt((x^3-27)/(4-x^2)) ?

The domain of f(x)=sqrt((x^3-27)/(4-x^2)) is x<-2\lor 2<x<= 3

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domain of f(x)=sqrt((x^3-27)/(4-x^2))

domain

f (x) = \frac{x ^{3} - 27}{4 - x ^{2}}

x < - 2 or 2 < x \leq 3

Interval Notation

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

Solution steps

Find non-negative values for radicals:

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

x < - 2 or 2 < x \leq 3

What is the domain of f(x)=sqrt((x^3-27)/(4-x^2)) ?
The domain of f(x)=sqrt((x^3-27)/(4-x^2)) is x<-2\lor 2<x<= 3