# Functions

**Algebra**Level 5

\[ \begin{cases} f_1(x)=x \\ f_2(x)=1-x \\ f_3(x)=\frac 1x \\ f_4(x)=\frac x{x-1} \\ f_5(x)=1-\frac 1x \\ f_6(x)=\frac 1{1-x} \end{cases} \]

Here we define 6 functions as shown above.

\((\{f_1,f_2,...,f_6\},\circ)\), where \(\circ\) being the function composition, defines a group.

This group is isomorphic to \(\text{__________} \).