In Java

1. Consider the function f:{1,2,3,4}{1,2,3,4} given by f(n)=(14213344) (a) Find f(1). (b) Find an element n in the domain such that f(n)=1. (c) Find an element n of the domain such that f(n)=n. (d) Find an element of the codomain that is not in the range. 2. The following functions all have {1,2,3,4,5} as both their domain and codomain. For each, determine whether it is (only) injective, (only) surjective, bijective, or neither injective nor surjective. (a) f=(1323334353). (b) f=(1223314554). (c) f(x)=6x. (d) f(x)={x/2(x+1)/2ifxisevenifxisodd. 3. The following functions all have domain {1,2,3,4,5} and codomain {1,2,3}. For each, determine whether it is (only) injective, (only) surjective, bijective, or neither injective nor surjective. (a) f=(1122314251). (b) f=(1122334152). (c) f(x)={xx3ifx3ifx>3. 4. The following functions all have domain {1,2,3,4} and codomain {1,2,3,4,5}. For each, determine whether it is (only) injective, (only) surjective, bijective, or neither injective nor surjective. (a) f=(11223544). 0. Introduction and Preliminaries (b) f=(11223342). (c) f(x) gives the number of letters in the English word for the number x. For example, f(1)=3 since "one" contains three letters. 5. Write out all functions f:{1,2,3}{a,b} (using two-line notation). How many functions are there? How many are injective? How many are surjective? How many are bijective