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

The domain of 1/(1-sqrt(x+1)) is -1 0

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domain of 1/(1-sqrt(x+1))

domain

\frac{1}{1 - x + 1}

- 1 \leq x < 0 or x > 0

Interval Notation

[- 1, 0) \cup (0, \infty)

Solution steps

Find non-negative values for radicals:

x \geq - 1

Find undefined (singularity) points:

x = 0

Combine real regions and undefined points for final function domain

- 1 \leq x < 0 or x > 0

What is the domain of 1/(1-sqrt(x+1)) ?
The domain of 1/(1-sqrt(x+1)) is -1<= x<0\lor x>0