What is the domain of f(x)=sqrt((36-x^2)/(x+1)) ?

The domain of f(x)=sqrt((36-x^2)/(x+1)) is x<=-6\lor-1<x<= 6

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domain of f(x)=sqrt((36-x^2)/(x+1))

domain

x \leq - 6 or - 1 < x \leq 6

Interval Notation

Solution steps

Find non-negative values for radicals:

x \leq - 6 or - 1 < x \leq 6

Find undefined (singularity) points:

x = - 1

Combine real regions and undefined points for final function domain

x \leq - 6 or - 1 < x \leq 6

What is the domain of f(x)=sqrt((36-x^2)/(x+1)) ?
The domain of f(x)=sqrt((36-x^2)/(x+1)) is x<=-6\lor-1<x<= 6