Question

32. On the set of integers \( Z \), define \( f: Z \rightarrow Z \) as \( f(x)=\left\{\begin{array}{ll}\frac{x}{2}, & x \text { is even } \\ 0, & x \text { is odd }\end{array}\right. \) Then, \( f \) is

Answer 1

f(x) = \( \begin{cases} \frac x2 & {,x = 2n; n\in N }\\ 0 & {x\, is \,odd} \end{cases}\)

= \( \begin{cases} n, & {n\in N, x \, is \, even \, s.t. \, x = 2n }\\ 0, & {x\, is \,odd} \end{cases}\)

\(\therefore\) f (x) is a whole number