Let a, b, c, d eR be real numbers, and consider the function ar + b...

 

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Let a, b, c, d eR be real numbers, and consider the function ar + b f: X R, aH cx +d with domain X = {r| ca + d+ 0}. %3D a) Show that f is injective if and only if ad – bc + 0. b) When this condition holds, find the range Y of the function f, and compute the inverse f1:Y → R. c) What can you say about f if ad – bc = 0? Let a, b, c, d eR be real numbers, and consider the function ar + b f: X R, aH cx +d with domain X = {r| ca + d+ 0}. %3D a) Show that f is injective if and only if ad – bc + 0. b) When this condition holds, find the range Y of the function f, and compute the inverse f1:Y → R. c) What can you say about f if ad – bc = 0?