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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].



Answer :

GinnyAnswer
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].

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