To determine the value of [tex]\((f \circ g)(10)\)[/tex], we need to follow these steps:
1. Identify the functions [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex]:
- [tex]\( f(x) = x^2 + 1 \)[/tex]
- [tex]\( g(x) = x - 4 \)[/tex]
2. Calculate [tex]\( g(10) \)[/tex]:
- Substitute [tex]\( x = 10 \)[/tex] into the function [tex]\( g \)[/tex]:
[tex]\[
g(10) = 10 - 4 = 6
\][/tex]
3. Calculate [tex]\( f(g(10)) \)[/tex]:
- We found that [tex]\( g(10) = 6 \)[/tex] in the previous step.
- Now, substitute [tex]\( x = 6 \)[/tex] into the function [tex]\( f \)[/tex]:
[tex]\[
f(6) = 6^2 + 1 = 36 + 1 = 37
\][/tex]
Therefore, the value of [tex]\((f \circ g)(10)\)[/tex] is [tex]\( f(g(10)) \)[/tex], which is [tex]\( 37 \)[/tex]. So, the equivalent value is:
[tex]\[
(f \circ g)(10) = 37
\][/tex]
