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The inverse function `g^(-1)(y)` is a function such that `g(g^(-1)(y))` = y and `g^(-1)(g(x)) = x.` To find it, we need to solve for x the equation

`g(x) = y,` in this case it is `-2x+4 = y.`

It is simple: `-2x = y-4,`  `2x = -y+4,`  `x = -1/2 y + 2.` You can check the above equalities from the definition of an inverse function.

The answer: the inverse function is `g^(-1)(y) = -1/2 y + 2.`

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