The function g is defined by g : x --> 2x^{2}- 8x + 11 for x<= A, where A is a constant.

Part (1) State the largest value of A for which g has an inverse.

Part (2) When A has this value, obtain an expression, in terms f x, for g^{-1}(x) and state the range of g^{-1}

Please explain both of these parts and explain the 2nd part in detail. Thank you.