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8

Part of 1978 Romania Team Selection Test

Problems(1)

fog=hog (similar functions)

Source: Romanian TST 1978, Day 1, P8

9/28/2018
For any set A A we say that two functions f,g:A⟶A f,g:A\longrightarrow A are similar, if there exists a bijection h:A⟶A h:A\longrightarrow A such that f∘h=h∘g. f\circ h=h\circ g.
a) If A A has three elements, construct a finite, arbitrary number functions, having as domain and codomain A, A, that are two by two similar, and every other function with the same domain and codomain as the ones determined is similar to, at least, one of them. b) For A=R, A=\mathbb{R} , show that the functions sin⁡ \sin and −sin⁡ -\sin are similar.
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