Answer :
To find: g : Z → Z : g o f = IZ
Formula used: (i) f o g = f(g(x))
(ii) g o f = g(f(x))
Given: (i) g : Z → Z : g o f = IZ
Solution: We have,
f(x) = 2x
Let f(x) = y
⇒ y = 2x
Where g: Z → Z
For g o f,
⇒ g(f(x))
⇒ g(2x)
⇒ x = IZ
Clearly we can see that (g o f) = x = IZ
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