To determine the value of [tex]$(f \circ g)(10)$[/tex], we need to evaluate the composite function [tex]$f(g(10))$[/tex] by following these steps:
1. Evaluate [tex]\( g(10) \)[/tex]:
- Start by calculating [tex]\( g(10) \)[/tex], where the function [tex]\( g \)[/tex] is defined as [tex]\( g(x) = x - 4 \)[/tex].
- Substitute 10 into [tex]\( g(x) \)[/tex]:
[tex]\[
g(10) = 10 - 4 = 6
\][/tex]
- So, [tex]\( g(10) = 6 \)[/tex].
2. Evaluate [tex]\( f(g(10)) \)[/tex]:
- Now that we have [tex]\( g(10) = 6 \)[/tex], we need to find [tex]\( f(6) \)[/tex].
- The function [tex]\( f \)[/tex] is defined as [tex]\( f(x) = x^2 + 1 \)[/tex].
- Substitute 6 into [tex]\( f(x) \)[/tex]:
[tex]\[
f(6) = 6^2 + 1 = 36 + 1 = 37
\][/tex]
- So, [tex]\( f(6) = 37 \)[/tex].
Therefore, the value equivalent to [tex]$(f \circ g)(10)$[/tex] is [tex]\( 37 \)[/tex].
