Find the inverse function of F(x) = 2 arcsinx

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Mira - To find an inverse, you simply swap the x and y values, then solve for y. In your problem you have y=2arcsin(x), so the inverse is x = 2arcsin(y).  Now just solve for y over the restricted domain [-1,1] x/2 = arcsin(y).   Solve for y by taking the sin of both sides of the equation.