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

The domain of y=arcsin(1/x) is x = 1

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domain of y=arcsin(1/x)

domain

y = arcsin (\frac{1}{x})

x \leq - 1 or x \geq 1

Interval Notation

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

Solution steps

Find known functions domain restrictions:

x \leq - 1 or x \geq 1

Find undefined (singularity) points:

x = 0

Combine real regions and undefined points for final function domain

x \leq - 1 or x \geq 1

f (t) = 4 - x

\frac{2 x ^{2} + 2 x - 12}{x ^{2} + 4 x - 5}

f (x) = \frac{x ^{2} + 5 x + 6}{x ^{2} + 9}

f (x) = - 4 x + 20

4 x^{3} + x

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