The ellipse shown below is defined by the equation 4 x 2 + y 2 = 4 4x^2+y^2=4 4 x 2 + y 2 = 4 . It consists of four one-to-one functions: g 1 ( x ) g_1\left(x\right) g 1 ( x ) , g 2 ( x ) g_2\left(x\right) g 2 ( x ) , g 3 ( x ) g_3\left(x\right) g 3 ( x ) , and g 4 ( x ) g_4\left(x\right) . What is the inverse function of g 4 ( x ) g_4\left(x\right) ? What is the domain of the inverse function?

g 4 − 1 ( x ) = 1 − x 2 4 g_4^{-1}\left(x\right)=\sqrt{1-\frac{x^2}{4}} Domain: − 2 ≤ x ≤ 0 -2\le x\le0 − 2 ≤ x ≤ 0

g 4 − 1 ( x ) = − 1 − x 2 4 g_4^{-1}\left(x\right)=-\sqrt{1-\frac{x^2}{4}} Domain: 0 ≤ x ≤ 2 0\le x\le2 0 ≤ x ≤ 2

g 4 − 1 ( x ) = 1 − x 2 4 g_4^{-1}\left(x\right)=\sqrt{1-\frac{x^2}{4}} Domain: 0 ≤ x ≤ 2 0\le x\le2

g 4 − 1 ( x ) = − 1 − x 2 4 g_4^{-1}\left(x\right)=-\sqrt{1-\frac{x^2}{4}} Domain: − 2 ≤ x ≤ 0 -2\le x\le0 − 2 ≤ x ≤ 0

The ellipse shown below is defined by the equation...

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