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

The domain of f(x)=sqrt(((5-x))/((x+3))) is -3<x<= 5

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

domain

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

- 3 < x \leq 5

Interval Notation

(- 3, 5]

Solution steps

Find non-negative values for radicals:

- 3 < x \leq 5

Find undefined (singularity) points:

x = - 3

Combine real regions and undefined points for final function domain

- 3 < x \leq 5

What is the domain of f(x)=sqrt(((5-x))/((x+3))) ?
The domain of f(x)=sqrt(((5-x))/((x+3))) is -3<x<= 5