# Functions-17

### From Homeworkwiki

**Let f : Z → Z, g : Z → Z be functions defined by f = {(n,n ^{2}) : n ∈ Z}**

**G = {(n, |n|**

^{2}) : n ∈ Z}. Show that f = g.**Solution:** Clearly, domain of f = Domain of g = Z

And, Co-domain of f = Co-domain of g = Z

We have, f(n) = n^{2} and g(n) = |n|^{2} = n^{2} [since, |n|^{2} = n^{2}]

Therefore, f(n) = g(n) for all n ∈ Z.

Hence, f = g.