D[sub]f[/sub] = { (x,y) belong to R[sup]2[/sup] : y > 0 , (1-y[sup]2[/sup] ) [sup]1/2[/sup] < x < - (1-y[sup]2[/sup] ) [sup]1/2[/sup] } U { (x,y) belong to R[sup]2[/sup] :
y < 0 , - (1-y[sup]2[/sup] ) [sup]1/2[/sup] < x < (1-y[sup]2[/sup] ) [sup]1/2[/sup] }
The domain is on the right bounded by y=x , y=-x. y changes from x to -x. The left part of the domain is bounded by y=x, y=-x, y changes from -x to x.
]]>- (1-y²)[sup]1/2[/sup]< x < (1-y²)[sup]1/2[/sup] , which is definitely wrong!
Perhaps three sets , as you suggested, is more logical.
]]>f(x,y) = Ln [ y / ( x[sup]2[/sup] + y[sup]2[/sup] -1 ) ]
D[sub]f[/sub] = { (x,y) belong to R[sup]2[/sup] : y > 0 , (1-y[sup]2[/sup] ) [sup]1/2[/sup] < x < - (1-y[sup]2[/sup] ) [sup]1/2[/sup] } U { (x,y) belong to R[sup]2[/sup] :
y < 0 , - (1-y[sup]2[/sup] ) [sup]1/2[/sup] < x < (1-y[sup]2[/sup] ) [sup]1/2[/sup] }
Thanks,
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