Check the injectivity and surjectivity of the following functions:
(i) `f : N ->N`given by `f(x)=x^2`
(ii) `f : Z-> Z`given by `f(x)=x^2`
(iii) `f : R ->R`given by `f(x)=x^2`
(iv) `f : N-> N`given by `f(x)=x^3`
(v) `f : Z → Z` given by `f(x) = x^3`

Explanation

To determine the injectivity and surjectivity of the given functions, we will analyze each function step by step.

### (i) Function: \( f: \mathbb{N} \to \mathbb{N} \) given by \( f(x) = x^2 \)

**Step 1: Check Injectivity**
- Assume \( f(x_1) = f(x_2) \).
- This implies \( x_1^2 = x_2^2 \).
- Since \( x_1, x_2 \in \mathbb{N} \), we can conclude that \( x_1 = x_2 \).
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