What is the domain of sqrt((16-x^2)/(x+1)) ?

The domain of sqrt((16-x^2)/(x+1)) is x<=-4\lor-1<x<= 4

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domain of sqrt((16-x^2)/(x+1))

domain

\frac{16 - x ^{2}}{x + 1}

x \leq - 4 or - 1 < x \leq 4

Interval Notation

(- \infty, - 4] \cup (- 1, 4]

Solution steps

Find non-negative values for radicals:

x \leq - 4 or - 1 < x \leq 4

Find undefined (singularity) points:

x = - 1

Combine real regions and undefined points for final function domain

x \leq - 4 or - 1 < x \leq 4

f (x) = x^{3} - 8

f (x) = \frac{x}{x ^{3} - 1}

x 36 - x^{2}

f (x) = 17 - 5 x

x^{3} - 4

What is the domain of sqrt((16-x^2)/(x+1)) ?
The domain of sqrt((16-x^2)/(x+1)) is x<=-4\lor-1<x<= 4