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

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

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

domain

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

x \leq \frac{1}{2}

Interval Notation

(- \infty, \frac{1}{2}]

Solution steps

Find known functions domain restrictions:

x \leq \frac{1}{2}

Find undefined (singularity) points:

x = 1

Combine real regions and undefined points for final function domain

x \leq \frac{1}{2}

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

x^{2} \cdot ln (x)

f (x) = \frac{x - 12}{2 ( x - 6 ) x - 6}

f (x) = 12 x^{2} - 7 x + 1

f (x) = 2 x + 1, x > 3

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