Given the function $P(x) = x + 3$, we are asked to find $P(x) + P(-x)$.

1. First, we evaluate $P(x)$: $P(x) = x + 3$

2. Now, evaluate $P(-x)$: $P(-x) = (-x) + 3 = -x + 3$

3. Next, add $P(x)$ and $P(-x)$: $P(x) + P(-x) = (x + 3) + (-x + 3)$ Simplifying the expression: $P(x) + P(-x) = x - x + 3 + 3 = 6$

Thus, $P(x) + P(-x) = 6$.

Would you like further details or have any questions?

Here are five related questions:

1. What would $P(x) + P(-x)$ be if $P(x) = x^2 + 3$?
2. How does $P(x) + P(-x)$ behave for odd and even functions?
3. Can you generalize $P(x) + P(-x)$ for any linear function?
4. What happens if we subtract $P(-x)$ from $P(x)$?
5. How would the result change if $P(x) = x^3 + 3$?

Tip: When adding functions like $P(x) + P(-x)$, look for symmetry in the function to simplify calculations.