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

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

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domain of f(x)=(sqrt(x+3))/(1-sqrt(x+2))

domain

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

- 2 \leq x < - 1 or x > - 1

Interval Notation

Solution steps

Find non-negative values for radicals:

x \geq - 2

Find undefined (singularity) points:

x = - 1

Combine real regions and undefined points for final function domain

- 2 \leq x < - 1 or x > - 1

y = - 2 x^{2} + 3

f (x) = \frac{x}{1 - e ^{x^{2} - 9}}

\frac{1}{2} - \frac{1}{2} cos (2 x - \frac{π}{4})

\frac{15 x - 15}{x ^{2} + 3 x - 4}

ln (\frac{x + 1}{x - 2})

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