Construct the composition table for the composition of functions `(o)` defined on the `S={f_1,\ f_2,\ f_3,\ f_4}` of four functions from `C` (the set of all complex numbers) to itself, defined by `f_1(z)=z ,\ \ f_2(z)=-z ,\ \ f_3(z)=1/z ,\ \ f_4(z)=-1/z` for all `z in Cdot`

Explanation

To construct the composition table for the functions defined on the set \( S = \{ f_1, f_2, f_3, f_4 \} \), we will compute the composition of each pair of functions. The functions are defined as follows:

- \( f_1(z) = z \)
- \( f_2(z) = -z \)
- \( f_3(z) = \frac{1}{z} \)
- \( f_4(z) = -\frac{1}{z} \)

We will denote the composition of functions \( f_i \) and \( f_j \) as \( f_i \circ f_j \).
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