What is the domain of f(x)=((sqrt(12-x-x^2)))/(x+2) ?

The domain of f(x)=((sqrt(12-x-x^2)))/(x+2) is -4<= x<-2\lor-2<x<= 3

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domain of f(x)=((sqrt(12-x-x^2)))/(x+2)

domain

f (x) = \frac{( 12 - x - x ^{2} )}{x + 2}

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

Interval Notation

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

Solution steps

Find non-negative values for radicals:

- 4 \leq x \leq 3

Find undefined (singularity) points:

x = - 2

Combine real regions and undefined points for final function domain

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

What is the domain of f(x)=((sqrt(12-x-x^2)))/(x+2) ?
The domain of f(x)=((sqrt(12-x-x^2)))/(x+2) is -4<= x<-2\lor-2<x<= 3