The answers to exercise marked [BB] can he found in the Back of the Book.Let A denote the...

The answers to exercise marked [BB] can he found in the Back of the Book.

Let A denote the set R \ {0, 1}. Let ι denote the identity function on A and define the functions ƒ, g, h, s, r : A → A by

(a) Show that ƒ o g = ι and g o r = s. Complete the table, thereby showing that the composition of any two of the given functions is one of the given five, or the identity.3

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(b) Which of the given six functions have inverses? Find (and identify) any inverses that exist.