Answered

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10. If [tex][tex]$p(x) = x + 3$[/tex][/tex], then [tex][tex]$p(x) + p(-x)$[/tex][/tex] is equal to:

a) 3

b) [tex][tex]$2x$[/tex][/tex]

c) 6

Sagot :

GinnyAnswer
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
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