# 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 $$\text{__________}$$.

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