Solution for Section 7.5 Question 3

3. a) Recall that the identity function for the integers is i_Z: ZZ  where i_Z(x) = x for all xZ.  

( f o i_Z )(x) = f (i_Z(x)) = f (x) = x + 1.

( i_Z o f )(x) = i_Z( f (x)) = i_Z(x + 1) = x + 1.

b) If  g: XX  is any function,  the functions  g o i_X and i_X o g  are both equal to the function g.

( g o i_X )(x) = g( i_X(x)) = g(x)   and   ( i_X o g )(x) = i_X( g(x)) = g(x).

Back to Section 7.5