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

The domain of f(x)= 1/(x-sqrt(1-x^2)) is -1<= x< 1/(sqrt(2))\lor 1/(sqrt(2))<x<= 1

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

domain

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

- 1 \leq x < \frac{1}{2} or \frac{1}{2} < x \leq 1

Interval Notation

[- 1, \frac{1}{2}) \cup (\frac{1}{2}, 1]

Solution steps

Find non-negative values for radicals:

- 1 \leq x \leq 1

Find undefined (singularity) points:

x = \frac{1}{2}

Combine real regions and undefined points for final function domain

- 1 \leq x < \frac{1}{2} or \frac{1}{2} < x \leq 1

8 x - 4 y = 8

\frac{1}{( x + 5 )}

x^{5}

f (x) = (4 - 10 x)^{\frac{5}{2}}

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