Answer :
To find the value of [tex]\( p(x) + p(-x) \)[/tex] given that [tex]\( p(x) = x + 3 \)[/tex], we will follow these steps:
1. Determine [tex]\( p(x) \)[/tex]:
The function [tex]\( p(x) \)[/tex] is defined as:
[tex]\[ p(x) = x + 3 \][/tex]
2. Determine [tex]\( p(-x) \)[/tex]:
Now, we need to find the value of the function when the input is [tex]\(-x\)[/tex]:
[tex]\[ p(-x) = -x + 3 \][/tex]
3. Calculate [tex]\( p(x) + p(-x) \)[/tex]:
We add [tex]\( p(x) \)[/tex] and [tex]\( p(-x) \)[/tex]:
[tex]\[ p(x) + p(-x) = (x + 3) + (-x + 3) \][/tex]
Simplifying this expression:
[tex]\[ p(x) + p(-x) = x + 3 - x + 3 = 6 \][/tex]
Therefore, the value of [tex]\( p(x) + p(-x) \)[/tex] is [tex]\(\boxed{6}\)[/tex].
1. Determine [tex]\( p(x) \)[/tex]:
The function [tex]\( p(x) \)[/tex] is defined as:
[tex]\[ p(x) = x + 3 \][/tex]
2. Determine [tex]\( p(-x) \)[/tex]:
Now, we need to find the value of the function when the input is [tex]\(-x\)[/tex]:
[tex]\[ p(-x) = -x + 3 \][/tex]
3. Calculate [tex]\( p(x) + p(-x) \)[/tex]:
We add [tex]\( p(x) \)[/tex] and [tex]\( p(-x) \)[/tex]:
[tex]\[ p(x) + p(-x) = (x + 3) + (-x + 3) \][/tex]
Simplifying this expression:
[tex]\[ p(x) + p(-x) = x + 3 - x + 3 = 6 \][/tex]
Therefore, the value of [tex]\( p(x) + p(-x) \)[/tex] is [tex]\(\boxed{6}\)[/tex].
