What is the domain of f(x)=sqrt((9-x)/(x+4)) ?

The domain of f(x)=sqrt((9-x)/(x+4)) is -4<x<= 9

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domain of f(x)=sqrt((9-x)/(x+4))

domain

f (x) = \frac{9 - x}{x + 4}

- 4 < x \leq 9

Interval Notation

(- 4, 9]

Solution steps

Find non-negative values for radicals:

- 4 < x \leq 9

Find undefined (singularity) points:

x = - 4

Combine real regions and undefined points for final function domain

- 4 < x \leq 9

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

f (x) = x^{2} + 3, x \leq 0

f (x) = \frac{x ^{2} + 6 x - 16}{x ^{2} - 4}

x^{2} - 4 x + 8

f (x) = \frac{7 x ^{2} + 16}{x ^{2} - 16}

What is the domain of f(x)=sqrt((9-x)/(x+4)) ?
The domain of f(x)=sqrt((9-x)/(x+4)) is -4<x<= 9