Question

Consider the set of all functions ƒ of the form f: {1, 2, 3, 4} → {1, 2, 3, 4, 5, 6}.

(a) How many functions are there total?

Answer 1

There are a total of 1296 functions.

Step-by-step explanation:

To find the total number of functions, we need to consider that each input value in the domain has 6 possible output values in the codomain. Therefore, for each input value, there are 6 choices. Since there are 4 input values, we multiply the number of choices for each input value: 6 x 6 x 6 x 6 = 1296. Therefore, there are a total of 1296 functions.