What is the domain of f(x)=sqrt((5-x)/(x^2-9)) ?

The domain of f(x)=sqrt((5-x)/(x^2-9)) is x<-3\lor 3<x<= 5

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domain of f(x)=sqrt((5-x)/(x^2-9))

domain

x < - 3 or 3 < x \leq 5

Interval Notation

Solution steps

Find non-negative values for radicals:

x < - 3 or 3 < x \leq 5

Find undefined (singularity) points:

x = 3, x = - 3

Combine real regions and undefined points for final function domain

x < - 3 or 3 < x \leq 5

What is the domain of f(x)=sqrt((5-x)/(x^2-9)) ?
The domain of f(x)=sqrt((5-x)/(x^2-9)) is x<-3\lor 3<x<= 5