To find and simplify the function [tex]\((f + g)(10)\)[/tex], given that [tex]\( f(x) = x + 4 \)[/tex] and [tex]\( g(x) = x^2 + 2 \)[/tex], we need to evaluate each function at [tex]\( x = 10 \)[/tex] and then sum the results.
Step-by-step solution:
1. Evaluate [tex]\( f(10) \)[/tex]:
[tex]\[
f(x) = x + 4
\][/tex]
Substitute [tex]\( x = 10 \)[/tex]:
[tex]\[
f(10) = 10 + 4 = 14
\][/tex]
2. Evaluate [tex]\( g(10) \)[/tex]:
[tex]\[
g(x) = x^2 + 2
\][/tex]
Substitute [tex]\( x = 10 \)[/tex]:
[tex]\[
g(10) = 10^2 + 2 = 100 + 2 = 102
\][/tex]
3. Sum the results to find [tex]\((f + g)(10)\)[/tex]:
[tex]\[
(f + g)(10) = f(10) + g(10)
\][/tex]
Substitute the values we found:
[tex]\[
(f + g)(10) = 14 + 102 = 116
\][/tex]
Therefore, [tex]\((f + g)(10) = 116\)[/tex].
