i. Show that if f : R R is a strictly increasing function and u...

 

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i. Show that if f : R → R is a strictly increasing function and u : R → R is a utility function that represents the preference relation E, then the function v : R' → R defined by v(x) = f(u(x)) (that is v = fou) is also a utility function representing the preference relation E. ii. Show that if f : R - R' is a strictly monotonic function and u : R- → R is a utility function that represents the preference relation E, then the function v : R → R defined by v(x) = is v = u o f) does not always represents the preference . [Hint: in order to show that something is not satisfied, you only need to provide an example] u(f(x)) (that 2. i. Show that if f : R → R is a strictly increasing function and u : R → R is a utility function that represents the preference relation E, then the function v : R' → R defined by v(x) = f(u(x)) (that is v = fou) is also a utility function representing the preference relation E. ii. Show that if f : R - R' is a strictly monotonic function and u : R- → R is a utility function that represents the preference relation E, then the function v : R → R defined by v(x) = is v = u o f) does not always represents the preference . [Hint: in order to show that something is not satisfied, you only need to provide an example] u(f(x)) (that 2.

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Consider the given problem here UX be the utility function and f be the strictly increasing ... View the full answer