Answer :
To determine the value of [tex]\( p(x) + p(-x) \)[/tex] given the function [tex]\( p(x) = x + 3 \)[/tex], let's follow these steps:
1. Define the function:
[tex]\( p(x) = x + 3 \)[/tex]
2. Calculate [tex]\( p(-x) \)[/tex]:
Substitute [tex]\(-x\)[/tex] for [tex]\( x \)[/tex] in the function [tex]\( p(x) \)[/tex]:
[tex]\[ p(-x) = (-x) + 3 = -x + 3 \][/tex]
3. Add [tex]\( p(x) \)[/tex] and [tex]\( p(-x) \)[/tex]:
[tex]\[ p(x) + p(-x) = (x + 3) + (-x + 3) \][/tex]
4. Combine like terms:
[tex]\[ p(x) + p(-x) = x + 3 - x + 3 \][/tex]
Simplify the expression:
[tex]\[ p(x) + p(-x) = 6 \][/tex]
Therefore, the value of [tex]\( p(x) + p(-x) \)[/tex] is [tex]\( 6 \)[/tex].
The correct answer is:
c) 6
1. Define the function:
[tex]\( p(x) = x + 3 \)[/tex]
2. Calculate [tex]\( p(-x) \)[/tex]:
Substitute [tex]\(-x\)[/tex] for [tex]\( x \)[/tex] in the function [tex]\( p(x) \)[/tex]:
[tex]\[ p(-x) = (-x) + 3 = -x + 3 \][/tex]
3. Add [tex]\( p(x) \)[/tex] and [tex]\( p(-x) \)[/tex]:
[tex]\[ p(x) + p(-x) = (x + 3) + (-x + 3) \][/tex]
4. Combine like terms:
[tex]\[ p(x) + p(-x) = x + 3 - x + 3 \][/tex]
Simplify the expression:
[tex]\[ p(x) + p(-x) = 6 \][/tex]
Therefore, the value of [tex]\( p(x) + p(-x) \)[/tex] is [tex]\( 6 \)[/tex].
The correct answer is:
c) 6
