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

The domain of arcsin(1/(1-x)) is x = 2

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domain of arcsin(1/(1-x))

domain

arcsin (\frac{1}{1 - x})

x \leq 0 or x \geq 2

Interval Notation

(- \infty, 0] \cup [2, \infty)

Solution steps

Find known functions domain restrictions:

x \leq 0 or x \geq 2

Find undefined (singularity) points:

x = 1

Combine real regions and undefined points for final function domain

x \leq 0 or x \geq 2

\frac{t - 2}{4 t - 12}

f (x) = \frac{5 x + 2}{x - 5}

f (x) = x^{2} - x - 12

y = \frac{2 x + 5}{9 x - 8}

y = \frac{x ^{4} - 16}{x ^{2} - 49}

What is the domain of arcsin(1/(1-x)) ?
The domain of arcsin(1/(1-x)) is x<= 0\lor x>= 2