To solve the problem [tex]\(10(f \circ g)(10)\)[/tex] given the functions [tex]\(f(x) = x^2 + 1\)[/tex] and [tex]\(g(x) = x - 4\)[/tex]:
1. Calculate [tex]\(g(10)\)[/tex]:
[tex]\[
g(10) = 10 - 4 = 6
\][/tex]
2. Use the result from [tex]\(g(10)\)[/tex] to find [tex]\(f(g(10))\)[/tex]:
[tex]\[
f(g(10)) = f(6)
\][/tex]
Now, substitute [tex]\(x\)[/tex] with 6 in the function [tex]\(f(x)\)[/tex]:
[tex]\[
f(6) = 6^2 + 1 = 36 + 1 = 37
\][/tex]
3. Finally, multiply this result by 10:
[tex]\[
10 \cdot f(g(10)) = 10 \cdot 37 = 370
\][/tex]
Thus, the value equivalent to [tex]\(10(f \circ g)(10)\)[/tex] is:
[tex]\[
\boxed{370}
\][/tex]
However, none of the provided options (37, 97, 126, 606) include 370. This suggests an error in the options given. Following the correct calculations, [tex]\(370\)[/tex] is indeed the result for [tex]\(10(f \circ g)(10)\)[/tex].
