Find the inverse of g(x)=-2x+4

Hello!
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.