- For each of the following, give an example of functions f: A g: B → C that satisfy the stated conditions, or explain why no such example » B and exists. * (a) The function f is a surjection, but the function go f is not a surjection. (b) The function f is an injection, but the function gof is not an injection. (c) The function g is a surjection, but the function g of is not a surjection. (d) The function g is an injection, but the function gof is not an injection. (e) The function f is not a surjection, but the function gof is a surjection. * (f) The function f is not an injection, but the function gof is an injection. (g) The function g is not a surjection, but the function go f is a surjection. (h) The function g is not an injection, but the function gof is an injection. 8. Let A be a nonempty set and let f: A A. For eachne N, define a = f and for each n e N. fo/? function f": A A recursively as follows: f' fo f! fof and f 3

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