What is the domain of f(x)=sqrt(2-(3x+11)/(x+5)) ?

The domain of f(x)=sqrt(2-(3x+11)/(x+5)) is -5<x<=-1

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domain of f(x)=sqrt(2-(3x+11)/(x+5))

domain

f (x) = 2 - \frac{3 x + 11}{x + 5}

- 5 < x \leq - 1

Interval Notation

Solution steps

Find non-negative values for radicals:

- 5 < x \leq - 1

Find undefined (singularity) points:

x = - 5

Combine real regions and undefined points for final function domain

- 5 < x \leq - 1

\frac{x - 2}{x ^{2} + 4}

3 sin (- 4 x - π) - 5

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

2 + x - 3

f (x) = x - 6 x + 1

What is the domain of f(x)=sqrt(2-(3x+11)/(x+5)) ?
The domain of f(x)=sqrt(2-(3x+11)/(x+5)) is -5<x<=-1