To find \(x\) from the given sets and conditions:

1. **Set G**:
\[
G = \{x = 2k + 1 \mid k \in \mathbb{N}, -1 \leq k \leq 2\}
\]

Since \(k\) is a natural number (\(\mathbb{N} \)), it must be \(k \geq 1\). In this context, we need to adjust for the range given (-1 to 2). As \(\mathbb{N}\) typically starts from 1, for practical purposes of this exercise, include 0 for exploration:

- \(k = 0 \Rightarrow x = 2(0) + 1 = 1\)
- \(k = 1 \Rightarrow x = 2(1) + 1 = 3\)
- \(k = 2 \Rightarrow x = 2(2) + 1 = 5\)

So, \( G = \{1, 3, 5\} \).

2. **Set F1**:
\[
F_1 = \{x \in \mathbb{R} \mid x^4 + 2x^3 - 6x^2 + 2x + 1 = 0\}
\]

This is a polynomial equation that generally requires numerical solutions or graphing software to find the roots.

3. **Set F2**:
\[
F_2 = \{x \in \mathbb{R} \mid x^4 - 8x^3 - 3x^2 + 32x - 4 = 0\}
\]

Similarly, this is another polynomial equation that requires specific solving methods such as graphing or numerical approximation.

Identifying \(x\) will depend on solving each polynomial equation for real roots, placing those solutions into \(\mathbb{R}\), and then comparing with set \(G\) if needed for common elements. Use numerical techniques or graphing tools for precise solutions.