Please answer this question and its subparts

3. (25 points) Part I11: Functions a. (7 pts) Consider functions f and g with the same domain X and co-domain Y, eg, f : X Y and gX -Y. Must it be true that fng is a function? Why or why not? glx) b. (4 pts) Draw an arrow diagram for a function that is injective but not surjective. , v/ c. (15 pts) Let S be the set of all strings having only O's and 1's. For example, O1 10101010 E S, etc. Define h: S Z as follows: for any s E S, S, 0011 E s h(s) = the number of l's in s minus the number of 0's in s 1. (3 points) What is h(101011)- h(00100) 2. (6 points) is h injective? Explain why or show a counter example. 3. (6 points) is h surjective? Explain why or show a counter example. Clearly label your answers to each part. 1 I Gan mp to G co domen D