Discuss the surjectivity of the following functions: `f: R->` given by` f(x)=x^3+2 `for all ` x in Rdot`

Explanation

To determine the surjectivity of the function \( f: \mathbb{R} \to \mathbb{R} \) defined by \( f(x) = x^3 + 2 \), we need to check whether every element in the codomain (which is \( \mathbb{R} \)) has a pre-image in the domain (also \( \mathbb{R} \)).

### Step-by-Step Solution:

1. **Identify the Function**:
We have the function \( f(x) = x^3 + 2 \).

2. **Determine the Range of the Function**:
...