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

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

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domain of f(x)=arcsin(1/(2x-1))

domain

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

x \leq 0 or x \geq 1

Interval Notation

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

Solution steps

Find known functions domain restrictions:

x \leq 0 or x \geq 1

Find undefined (singularity) points:

x = \frac{1}{2}

Combine real regions and undefined points for final function domain

x \leq 0 or x \geq 1

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