What is the domain of sqrt((36-x^2)/(x+3)) ?

The domain of sqrt((36-x^2)/(x+3)) is x<=-6\lor-3<x<= 6

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domain of sqrt((36-x^2)/(x+3))

domain

\frac{36 - x ^{2}}{x + 3}

x \leq - 6 or - 3 < x \leq 6

Interval Notation

(- \infty, - 6] \cup (- 3, 6]

Solution steps

Find non-negative values for radicals:

x \leq - 6 or - 3 < x \leq 6

Find undefined (singularity) points:

x = - 3

Combine real regions and undefined points for final function domain

x \leq - 6 or - 3 < x \leq 6

f (x) = \frac{- 3}{x ^{2}}

f (x) = \frac{x}{x ^{2} + 18}

f (x) = \frac{6 x}{x ^{2} - 1}

(1, 5), (9, 8)

(- 6, 8), (- 3, 9)

What is the domain of sqrt((36-x^2)/(x+3)) ?
The domain of sqrt((36-x^2)/(x+3)) is x<=-6\lor-3<x<= 6