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Check the nature of the following functi...

Check the nature of the following function.
(i) `f(x)=sin x, x in R " (ii) " f(x) =sin x, x in N`

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To check the nature of the given functions, we will analyze each case step by step. ### Part (i): \( f(x) = \sin x \), where \( x \in \mathbb{R} \) 1. **Definition of Many-One Function**: A function is many-one if there exist distinct values \( x_1 \) and \( x_2 \) in the domain such that \( f(x_1) = f(x_2) \). 2. **Setting Up the Equation**: Assume \( f(x_1) = f(x_2) \). This means: \[ ...
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