What is domain of arcsin(2x-1)?

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You need to remember that the domain of inverse function `arcsin (2x - 1)` is the interval `[-1,1]` , hence, you need to consider the following condition for the argument of the given function, such that:

`-1<=(2x - 1)<=1`

Adding `1` both sides, yields:

`1 - 1 <= 2x - 1 + 1 <= 1 + 1 => 0 <= 2x <= 2`

Dividing by `2` both sides, yields:

`0/2 <= (2x)/2 <= 2/2 => 0 <= x <= 1`

Hence, evaluating the domain of the given function, yields `x in [0,1]`

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