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I am not sure what the domain of $\displaystyle \arcsin \left(x - \frac{2}{3}\right)$ is.

I know that the domain for $\arcsin$ is $[-1, 1]$, but how can I use this to find the domain of the function above?

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To be more accurate, the function arcsin$(t)$ has domain $t\in [-1,1]$. Your function is arcsin$(t)$ where $t = x-2/3$. So you want to find values of $x$ such that $(x-2/3)\in [-1,1]$. –  andraiamatrix Jan 12 at 3:34
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Hint: what values of $x$ would make $\displaystyle x - \frac{2}{3}$ be within the domain of $\arcsin$?

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hmmm i see, thank you –  marck Jan 12 at 4:11
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