To find the value equivalent to [tex]\((f \circ g)(10)\)[/tex], we have to follow these steps:
1. Understand the functions:
[tex]\[
f(x) = x^2 + 1
\][/tex]
[tex]\[
g(x) = x - 4
\][/tex]
2. Calculate [tex]\( g(10) \)[/tex]:
[tex]\[
g(10) = 10 - 4 = 6
\][/tex]
3. Next, use the result from [tex]\( g(10) \)[/tex] as the input to the function [tex]\( f \)[/tex]:
[tex]\[
f(g(10)) = f(6)
\][/tex]
4. Calculate [tex]\( f(6) \)[/tex]:
[tex]\[
f(6) = 6^2 + 1 = 36 + 1 = 37
\][/tex]
Therefore, the value equivalent to [tex]\((f \circ g)(10)\)[/tex] is [tex]\(\boxed{37}\)[/tex].
