Answer :
To find the value of \( p(x) + p(-x) \) given the function \( p(x) = x + 4 \), we'll follow these steps:
1. Determine \( p(x) \):
Given \( p(x) = x + 4 \).
2. Determine \( p(-x) \):
Substitute \( -x \) into the function:
[tex]\[ p(-x) = -x + 4 \][/tex]
3. Sum \( p(x) \) and \( p(-x) \):
Add the expressions for \( p(x) \) and \( p(-x) \):
[tex]\[ p(x) + p(-x) = (x + 4) + (-x + 4) \][/tex]
4. Simplify the expression:
Combine the terms inside the parentheses:
[tex]\[ (x + 4) + (-x + 4) = x + 4 - x + 4 \][/tex]
Notice that \( x \) and \( -x \) will cancel each other out:
[tex]\[ x - x + 4 + 4 = 0 + 8 = 8 \][/tex]
Thus, the sum \( p(x) + p(-x) \) simplifies to 8.
So, \( p(x) + p(-x) \) is:
[tex]\[ \boxed{8} \][/tex]
1. Determine \( p(x) \):
Given \( p(x) = x + 4 \).
2. Determine \( p(-x) \):
Substitute \( -x \) into the function:
[tex]\[ p(-x) = -x + 4 \][/tex]
3. Sum \( p(x) \) and \( p(-x) \):
Add the expressions for \( p(x) \) and \( p(-x) \):
[tex]\[ p(x) + p(-x) = (x + 4) + (-x + 4) \][/tex]
4. Simplify the expression:
Combine the terms inside the parentheses:
[tex]\[ (x + 4) + (-x + 4) = x + 4 - x + 4 \][/tex]
Notice that \( x \) and \( -x \) will cancel each other out:
[tex]\[ x - x + 4 + 4 = 0 + 8 = 8 \][/tex]
Thus, the sum \( p(x) + p(-x) \) simplifies to 8.
So, \( p(x) + p(-x) \) is:
[tex]\[ \boxed{8} \][/tex]
