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Let ZZ be that set of integers and f:ZZ ...

Let `ZZ` be that set of integers and `f:ZZ rarr ZZ` be defined by `f(x)=2x,` for all ` x in ZZ` and g: `ZZ rarr ZZ` be defined by, (for all `x in ZZ)`
`g(x)={((x)/(2) " when x is even" ),(0" when x is odd" ):}`
Show that, `(g o f) =I_(ZZ)`, but `(f o g) ne I_(ZZ)`.

Text Solution

Verified by Experts

The correct Answer is:
`(f o g) (x) ne x, ` for all `x in ZZ i.e., (f o g) ne I_(ZZ)`
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