Find the range :
(i) `f(x) = 2x^(2)`
(ii) `f(x) = -x^(2)`

Explanation

To find the range of the given functions, we will analyze each function step by step.

### (i) For the function \( f(x) = 2x^2 \):

1. **Identify the function**: The function is \( f(x) = 2x^2 \).
2. **Determine the domain**: The domain of \( f(x) \) is all real numbers, \( x \in \mathbb{R} \).
3. **Analyze the function**: The term \( x^2 \) is always non-negative for all real \( x \) (i.e., \( x^2 \geq 0 \)).
4. **Multiply by 2**: Since \( 2 \) is a positive constant, multiplying \( x^2 \) by \( 2 \) will also yield a non-negative result. Thus, \( f(x) = 2x^2 \geq 0 \).
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