Hey,(adsbygoogle = window.adsbygoogle || []).push({});

Let ##(f,g) \in B^A## where ##A## and ##B## are non-empty sets, ##B^A## denotes the set of bijective functions between ##A## and ##B##.

We assume that there exists ##h_0: A \rightarrow A## and ##h_1: B \rightarrow B## such that ##f = h_1 \circ g \circ h_0 ##.

This implies that ##g = h^{-1}_1 \circ f \circ h^{-1}_0##, according to my teacher, but why is that?

We have that ##h^{-1}_1 \circ f = g \circ h^{-1}_0 ##, but how do I proceed from that?

I have drawn a graph with sets and arrows representing functions such that going from ##A## to ##B## via ##h_0##, ##g## and ##h_1## is the same as going from ##A## to ##B## via ##f##. I then manipulated this graph a little while maintaining the proper relations between the sets, which showed that going from ##A## to ##B## via ##g## is the same as going through (in order) ##h^{-1}_0##, ##f## and ##h^{-1}_1##, but this is hardly a proof at all.

Thanks

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Invert a triple composite function p(q(r(x)))

Loading...

Similar Threads - Invert triple composite | Date |
---|---|

A special invertible k-bits to n-bits mapping | Sep 29, 2011 |

Random variables that are triple-wise independent but quadruple-wise dependent | Dec 12, 2010 |

Inverting a Test Statistic | Dec 24, 2009 |

Set of non-invertible matrices is unbounded | May 3, 2009 |

Proof of pythagorean triple | Jan 25, 2009 |

**Physics Forums - The Fusion of Science and Community**