Invertible linear-fractional functions. Let f : R" → R" be the linear-fractional function f(x) = (Ax + b)/(c"x+d), dom f = {r | c"x +d >0}. %3D Suppose the matrix Q = cT d is nonsingular. Show that f is invertible and that f is a linear-fractional mapping. Give an explicit expression forf and its domain in terms of A, b, c, and d. Hint. It may be easier to express f in terms of Q.

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