Prove Theorem (b): If f is any function from a set X to a
Chapter 7, Problem 13E(choose chapter or problem)
Prove Theorem (b): If f is any function from a set X to a set Y, then IY o f = f, where IY is the identity function on Y.TheoremComposition with an Identity FunctionIf f is a function from a set X to a set Y, and IX is the identity function on X, and IY is the identity function on Y , then(a) f ? IX = f and (b) IY ? f = f.Proof:Part (a):Suppose f is a function from a set X to a set Y and IX is the identity function on X. Then, for all x in X,(f ? IX )(x)= f (IX (x))= f(x).Hence, by definition of equality of functions, f ? IX = f, as was to be shown.Part (b):This is exercise 13 at the end of this section.
Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.
Becoming a subscriber
Or look for another answer