What is the domain of f(x)=sqrt((9-x^2)/(x+1)) ?

The domain of f(x)=sqrt((9-x^2)/(x+1)) is x<=-3\lor-1<x<= 3

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domain of f(x)=sqrt((9-x^2)/(x+1))

domain

f (x) = \frac{9 - x ^{2}}{x + 1}

x \leq - 3 or - 1 < x \leq 3

Interval Notation

(- \infty, - 3] \cup (- 1, 3]

Solution steps

Find non-negative values for radicals:

x \leq - 3 or - 1 < x \leq 3

Find undefined (singularity) points:

x = - 1

Combine real regions and undefined points for final function domain

x \leq - 3 or - 1 < x \leq 3

What is the domain of f(x)=sqrt((9-x^2)/(x+1)) ?
The domain of f(x)=sqrt((9-x^2)/(x+1)) is x<=-3\lor-1<x<= 3