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

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

Sagot :

GinnyAnswer
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.
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