To determine [tex]\((f \circ g)(10)\)[/tex], we need to follow a step-by-step process by first evaluating [tex]\(g(10)\)[/tex] and then substituting this result into [tex]\(f(x)\)[/tex].
Here’s the step-by-step process:
1. Evaluate [tex]\(g(10)\)[/tex]:
The function [tex]\(g(x)\)[/tex] is defined as [tex]\(g(x) = x - 4\)[/tex].
Plug in [tex]\( x = 10 \)[/tex]:
[tex]\[
g(10) = 10 - 4 = 6
\][/tex]
2. Evaluate [tex]\(f(g(10))\)[/tex]:
Now, we substitute the result of [tex]\(g(10)\)[/tex] into [tex]\(f(x)\)[/tex]. The function [tex]\(f(x)\)[/tex] is defined as [tex]\(f(x) = x^2 + 1\)[/tex].
Since [tex]\(g(10) = 6\)[/tex], we need to find [tex]\(f(6)\)[/tex]:
[tex]\[
f(6) = 6^2 + 1 = 36 + 1 = 37
\][/tex]
Thus, the value of [tex]\((f \circ g)(10)\)[/tex] is [tex]\( 37 \)[/tex].
Therefore, the correct choice is 37.
