Real Analysis

Question
Let f:S\rightarrow s,.codecogs.com/gif.latex?f%3AS%5Crightarrow%20S%2C”> where S is the set of all integers, be defined byf(s)=as+b.codecogs.com/gif.latex?f%28s%29%3Das+b”>, where a, b are integers. Find the necessary and sufficient conditions on a, b in order that f\circ f=.codecogs.com/gif.latex?f%5Ccirc%20f%3Di_%7BS%7D”>

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