Given Functions:
P(x) = x³ + 3x² + 3x + 1
g(x) = x + 2

Explanation:

1. P(x) Function:
- P(x) is a cubic polynomial function with coefficients 1, 3, 3, and 1 for x³, x², x, and the constant term respectively.
- The function P(x) can be written as P(x) = x³ + 3x² + 3x + 1.

2. g(x) Function:
- g(x) is a linear function with a coefficient of 1 for x and a constant term of 2.
- The function g(x) can be written as g(x) = x + 2.

Relation between P(x) and g(x):
- The relation between P(x) and g(x) is that g(x) is a linear function while P(x) is a cubic polynomial function.
- There is no direct relationship or operation between P(x) and g(x) in the given information.

Conclusion:
- In conclusion, the functions P(x) = x³ + 3x² + 3x + 1 and g(x) = x + 2 are independent functions with different degrees and forms. They do not interact or affect each other in the given context.