What is the domain of f(x)=sqrt((16-x^2)/(x+3)) ?

The domain of f(x)=sqrt((16-x^2)/(x+3)) is x<=-4\lor-3<x<= 4

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domain of f(x)=sqrt((16-x^2)/(x+3))

domain

f (x) = \frac{16 - x ^{2}}{x + 3}

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

Interval Notation

(- \infty, - 4] \cup (- 3, 4]

Solution steps

Find non-negative values for radicals:

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

Find undefined (singularity) points:

x = - 3

Combine real regions and undefined points for final function domain

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

2 x - 3 y = 8

f (x) = 6 tan (0.2 x)

f (x) = \frac{3}{x + 4}

f (x) = 2 - 3 - x

f (x) = - 4 x^{3} + 2 x^{2} - 7

What is the domain of f(x)=sqrt((16-x^2)/(x+3)) ?
The domain of f(x)=sqrt((16-x^2)/(x+3)) is x<=-4\lor-3<x<= 4