A Function Invariant under a Group of Transformations

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The functions , , given by , , , , , and form a group with the composition of maps; for instance .


Moreover, if we take , we have , , that is, the function is invariant with respect to the group of transformations . The graph demonstrates this behaviour: choose a real number on the horizontal axis; the numbers , are shown on the same axis and the corresponding values (red points) are all at the same height.


Contributed by: Juan Luis Varona (March 2011)
Open content licensed under CC BY-NC-SA



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