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

The domain of f(x)=sqrt((5-x)/(x^2-x-2)) is x<-1\lor 2<x<= 5

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

domain

x < - 1 or 2 < x \leq 5

Interval Notation

(- \infty, - 1) \cup (2, 5]

Solution steps

Find non-negative values for radicals:

x < - 1 or 2 < x \leq 5

Find undefined (singularity) points:

x = 2, x = - 1

Combine real regions and undefined points for final function domain

x < - 1 or 2 < x \leq 5

What is the domain of f(x)=sqrt((5-x)/(x^2-x-2)) ?
The domain of f(x)=sqrt((5-x)/(x^2-x-2)) is x<-1\lor 2<x<= 5