What is the domain of f(x)=sqrt(-x)+1/(sqrt(2+x)) ?

The domain of f(x)=sqrt(-x)+1/(sqrt(2+x)) is -2<x<= 0

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domain of f(x)=sqrt(-x)+1/(sqrt(2+x))

domain

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

- 2 < x \leq 0

Solution steps

Find non-negative values for radicals:

- 2 \leq x \leq 0

Find undefined (singularity) points:

x = - 2

Combine real regions and undefined points for final function domain

- 2 < x \leq 0

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

f (x) = \frac{1}{x ^{2} + 2 x - 3}

- 3 x + 1

g (x) = 5 - 2 x

f (x) = ln (x^{2} - 16)

What is the domain of f(x)=sqrt(-x)+1/(sqrt(2+x)) ?
The domain of f(x)=sqrt(-x)+1/(sqrt(2+x)) is -2<x<= 0