If f(x) is a real valued function, then which of the following is injective function ?
(i) `f(x) = x^(5)` (ii) `f(x) = x + sin x`
(iii) `f(x) = x^(2)` (iv) `f(x) = e^(x)`
(v) `f(x) = x^(3) + x^(2) + 4x + 4`

Explanation

To determine which of the given functions are injective (one-to-one), we will analyze each function one by one. A function \( f(x) \) is injective if for any \( x_1 \) and \( x_2 \), \( f(x_1) = f(x_2) \) implies \( x_1 = x_2 \).

### Step 1: Analyze \( f(x) = x^5 \)

1. **Check if \( f(x_1) = f(x_2) \) implies \( x_1 = x_2 \)**:
\[ f(x_1) = f(x_2) \implies x_1^5 = x_2^5 \]
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