What is the domain of f(x)=(sqrt(9-x^2))/(x^2+7x+10) ?

The domain of f(x)=(sqrt(9-x^2))/(x^2+7x+10) is -3<= x<-2\lor-2<x<= 3

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domain of f(x)=(sqrt(9-x^2))/(x^2+7x+10)

domain

f (x) = \frac{9 - x ^{2}}{x ^{2} + 7 x + 10}

- 3 \leq x < - 2 or - 2 < x \leq 3

Interval Notation

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

Solution steps

Find non-negative values for radicals:

- 3 \leq x \leq 3

Find undefined (singularity) points:

x = - 2, x = - 5

Combine real regions and undefined points for final function domain

- 3 \leq x < - 2 or - 2 < x \leq 3

What is the domain of f(x)=(sqrt(9-x^2))/(x^2+7x+10) ?
The domain of f(x)=(sqrt(9-x^2))/(x^2+7x+10) is -3<= x<-2\lor-2<x<= 3