college trig

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I need to find the domain of the following function:

y=arcsin((x-3)/(2x+1))

My math is a bit rusty after holidays...This is what I did: (I'll use <> for the sign of 'not equal')

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

But i'm not sure about the rest! What I though of doing was this: the domain of arcsin(x) is [-1,1], so I could write that for the given function, ((x-3)/(2x+1)) is between -1 and 1... Not sure though...Help!

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