Let `f: ZvecZ` be defined by `f(n)=3n` for all `n in Z` and `g: Zvec` be defined by `f(n)={n/3,ifni samul t i p l eof3 0,ifni snotmul t i p l eof3fora l ln in Zdot` Show that `gof=I_Z` and `fog!=I_Z`

Explanation

It can be seen that,

`g(n){3n/3=n}`

So,

`g(n)=I_z`


And,

`F(n)=3g(n)={3` if n is a multiple of `3`,

`0` if n is not a multiple of `3}`

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