A2. Let the function u(t) be defined by at + b u(t) = ct + d'...

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A2. Let the function u(t) be defined by at + b u(t) = ct + d' with arbitrary (real valued) constant coefficients a, b, c, d. (a) Determine the domain for generic values of a, b, c, d. Are there any special value of these coefficients for which the domain is larger? (b) Determine a condition on the coefficients such that u is injective, and find th inverse function u function in that case. Hence, conclude what is the range of the function u for generic coefficients a, b, c, d. A2. Let the function u(t) be defined by at + b u(t) = ct + d' with arbitrary (real valued) constant coefficients a, b, c, d. (a) Determine the domain for generic values of a, b, c, d. Are there any special value of these coefficients for which the domain is larger? (b) Determine a condition on the coefficients such that u is injective, and find th inverse function u function in that case. Hence, conclude what is the range of the function u for generic coefficients a, b, c, d.