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

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

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

domain

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

x < 0 or 0 < x \leq 1

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \leq 1

Find undefined (singularity) points:

x = 0

Combine real regions and undefined points for final function domain

x < 0 or 0 < x \leq 1

f (x) = 3 x - 2 y = 12

y = \frac{30 - 6 x}{x ^{2} - 11 x + 30}

3 x - 1

\frac{2}{x - 3} - 2

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

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