If `f:R to R` be defined by `f(x) =2x+sinx ` for `x in R`, then check the nature of the function.

Explanation

To determine the nature of the function \( f: \mathbb{R} \to \mathbb{R} \) defined by \( f(x) = 2x + \sin x \), we will check if it is one-to-one (injective) and onto (surjective).

### Step 1: Finding the Derivative
First, we find the derivative of the function \( f(x) \):
\[ f'(x) = \frac{d}{dx}(2x + \sin x) = 2 + \cos x \]

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