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If f: Z->Z be defined by f(x)=2x for all...

If `f: Z->Z` be defined by `f(x)=2x` for all `x in Z` . Find `g: Z->Z` such that `gof=I_Z` .

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We have to find `g: Z->Z`
Let `x in Z`.
Then,
`(gof)=I_z=>(gof)(x)=I_z(x)`
`impliesg[f(x)]=x`
`impliesg(2x)=x`
`impliesg(y)=(1/2)y `
[where `2x=y`].
...
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