Answered

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If [tex]\( f(x) = x^2 + 1 \)[/tex] and [tex]\( g(x) = x - 4 \)[/tex], which value is equivalent to [tex]\( (f \circ g)(10) \)[/tex]?

A. 37
B. 97
C. 126
D. 606

Sagot :

GinnyAnswer
To solve the problem of finding [tex]\((f \circ g)(10)\)[/tex], where [tex]\(f(x) = x^2 + 1\)[/tex] and [tex]\(g(x) = x - 4\)[/tex], we will proceed step-by-step.

First, we need to understand what [tex]\((f \circ g)(10)\)[/tex] means. The notation [tex]\((f \circ g)(10)\)[/tex] is read as "f composed with g of 10." This means we will first apply the function [tex]\(g\)[/tex] to the number 10, and then we will apply the function [tex]\(f\)[/tex] to the result of [tex]\(g(10)\)[/tex].

1. Evaluate [tex]\(g(10)\)[/tex]:
[tex]\[ g(x) = x - 4 \][/tex]
Substituting [tex]\(x = 10\)[/tex]:
[tex]\[ g(10) = 10 - 4 = 6 \][/tex]

2. Next, evaluate [tex]\(f(g(10))\)[/tex] which is [tex]\(f(6)\)[/tex]:
[tex]\[ f(x) = x^2 + 1 \][/tex]
Substituting [tex]\(x = 6\)[/tex]:
[tex]\[ f(6) = 6^2 + 1 = 36 + 1 = 37 \][/tex]

Therefore, [tex]\((f \circ g)(10) = f(g(10)) = f(6) = 37\)[/tex].

The value equivalent to [tex]\((f \circ g)(10)\)[/tex] is [tex]\(\boxed{37}\)[/tex].
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