Answer :
To solve this problem, we're looking for the value of [tex]\((f \circ g)(10)\)[/tex]. This means we want to find the result of applying the function [tex]\(f\)[/tex] to the output of the function [tex]\(g\)[/tex] when [tex]\(x = 10\)[/tex].
Here's how you can solve it step-by-step:
1. Understand the Functions:
- We have two functions, [tex]\(f(x) = x^2 + 1\)[/tex] and [tex]\(g(x) = x - 4\)[/tex].
2. Evaluate [tex]\(g(10)\)[/tex]:
- Substitute [tex]\(10\)[/tex] into the function [tex]\(g(x)\)[/tex]:
[tex]\[
g(10) = 10 - 4 = 6
\][/tex]
3. Evaluate [tex]\(f(g(10))\)[/tex]:
- Now, substitute the result from [tex]\(g(10)\)[/tex] into the function [tex]\(f(x)\)[/tex]:
[tex]\[
f(6) = 6^2 + 1 = 36 + 1 = 37
\][/tex]
Therefore, the value of [tex]\((f \circ g)(10)\)[/tex] is [tex]\(\boxed{37}\)[/tex].
Here's how you can solve it step-by-step:
1. Understand the Functions:
- We have two functions, [tex]\(f(x) = x^2 + 1\)[/tex] and [tex]\(g(x) = x - 4\)[/tex].
2. Evaluate [tex]\(g(10)\)[/tex]:
- Substitute [tex]\(10\)[/tex] into the function [tex]\(g(x)\)[/tex]:
[tex]\[
g(10) = 10 - 4 = 6
\][/tex]
3. Evaluate [tex]\(f(g(10))\)[/tex]:
- Now, substitute the result from [tex]\(g(10)\)[/tex] into the function [tex]\(f(x)\)[/tex]:
[tex]\[
f(6) = 6^2 + 1 = 36 + 1 = 37
\][/tex]
Therefore, the value of [tex]\((f \circ g)(10)\)[/tex] is [tex]\(\boxed{37}\)[/tex].
