To find: g : Z → Z : g o f = I_Z

Formula used: (i) f o g = f(g(x))

(ii) g o f = g(f(x))

Given: (i) g : Z → Z : g o f = I_Z

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 = I_Z

Clearly we can see that (g o f) = x = I_Z