(Solved): Let \( f(x)=(3 x / 2) \). For this problem we use notation \( c \mathbb{Z} \) to denote the set of ...

Let \( f(x)=(3 x / 2) \). For this problem we use notation \( c \mathbb{Z} \) to denote the set of multiples of \( c \). Ex.: \( 2 \mathbb{Z} \) denotes even integers and \( 3 \mathbb{Z} \) denotes multiples of 3. a) Prove that \( \mathrm{f}: \mathbb{Z} \rightarrow \mathbb{Z} \) is not a function ( that is, it is not a function if both its domain and codomain are integers) b) Prove that \( \mathrm{f}: 2 \mathbb{Z} \rightarrow \mathbb{Z} \) is a function (that is, it is a function if its domain is even integers and its codomain is all integers)