To find [tex]\((f \circ g)(10)\)[/tex], we need to follow the steps of function composition, where we first apply the function [tex]\(g\)[/tex] to 10 and then apply the function [tex]\(f\)[/tex] to the result of [tex]\(g(10)\)[/tex].
Here are the given functions:
[tex]\[ g(x) = x - 4 \][/tex]
[tex]\[ f(x) = x^2 + 1 \][/tex]
1. Evaluate [tex]\(g(10)\)[/tex]:
[tex]\[ g(10) = 10 - 4 = 6 \][/tex]
2. Now, evaluate [tex]\(f\)[/tex] at the value obtained from [tex]\(g(10)\)[/tex]:
[tex]\[ f(g(10)) = f(6) \][/tex]
3. To find [tex]\(f(6)\)[/tex], plug in 6 into the function [tex]\(f\)[/tex]:
[tex]\[ f(6) = 6^2 + 1 = 36 + 1 = 37 \][/tex]
Therefore, [tex]\((f \circ g)(10)\)[/tex] is equal to 37.
The correct answer is 37.
