What is the domain of f(x)=sqrt((5-4x-x^2)/(x+3)) ?

The domain of f(x)=sqrt((5-4x-x^2)/(x+3)) is x<=-5\lor-3<x<= 1

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domain of f(x)=sqrt((5-4x-x^2)/(x+3))

domain

f (x) = \frac{5 - 4 x - x ^{2}}{x + 3}

x \leq - 5 or - 3 < x \leq 1

Interval Notation

(- \infty, - 5] \cup (- 3, 1]

Solution steps

Find non-negative values for radicals:

x \leq - 5 or - 3 < x \leq 1

Find undefined (singularity) points:

x = - 3

Combine real regions and undefined points for final function domain

x \leq - 5 or - 3 < x \leq 1

- \frac{x ^{2}}{10} + \frac{9 x}{10} + \frac{11}{5}

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

f (x) = \frac{6 x}{x ^{2} + 16}

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

(- 4, 3), (1, - 4)

What is the domain of f(x)=sqrt((5-4x-x^2)/(x+3)) ?
The domain of f(x)=sqrt((5-4x-x^2)/(x+3)) is x<=-5\lor-3<x<= 1