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

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

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

domain

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

- 1 \leq x < 0 or 0 < x \leq 1

Interval Notation

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

Solution steps

Find non-negative values for radicals:

- 1 \leq x \leq 1

Find undefined (singularity) points:

x = 0

Combine real regions and undefined points for final function domain

- 1 \leq x < 0 or 0 < x \leq 1

\frac{1}{x + 7}

f (x) = \frac{7 x}{x ^{2} + 49}

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

f (x) = 2 x^{2} - 5 x + 1

\frac{2}{3 - x}

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