To find the value of [tex]\( f(x) + f(-x) \)[/tex] for the function [tex]\( f(x) = x + 3 \)[/tex], follow these steps:
1. Define the function [tex]\( f(x) \)[/tex]:
The given function is [tex]\( f(x) = x + 3 \)[/tex].
2. Evaluate [tex]\( f(x) \)[/tex]:
By substituting [tex]\( x \)[/tex] into the function, we get:
[tex]\[
f(x) = x + 3
\][/tex]
3. Evaluate [tex]\( f(-x) \)[/tex]:
Substitute [tex]\(-x\)[/tex] into the function:
[tex]\[
f(-x) = (-x) + 3 = -x + 3
\][/tex]
4. Sum the results [tex]\( f(x) \)[/tex] and [tex]\( f(-x) \)[/tex]:
Add the expressions for [tex]\( f(x) \)[/tex] and [tex]\( f(-x) \)[/tex]:
[tex]\[
f(x) + f(-x) = (x + 3) + (-x + 3)
\][/tex]
5. Combine the like terms:
Simplify the expression by combining the terms:
[tex]\[
f(x) + f(-x) = x + 3 - x + 3 = 3 + 3 = 6
\][/tex]
Therefore, the value of [tex]\( f(x) + f(-x) \)[/tex] is:
[tex]\[
\boxed{6}
\][/tex]
