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Unit Test

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 :

To find the value equivalent to [tex]\((f \circ g)(10)\)[/tex], we have to follow these steps:

1. Understand the functions:
[tex]\[ f(x) = x^2 + 1 \][/tex]
[tex]\[ g(x) = x - 4 \][/tex]

2. Calculate [tex]\( g(10) \)[/tex]:
[tex]\[ g(10) = 10 - 4 = 6 \][/tex]

3. Next, use the result from [tex]\( g(10) \)[/tex] as the input to the function [tex]\( f \)[/tex]:
[tex]\[ f(g(10)) = f(6) \][/tex]

4. Calculate [tex]\( f(6) \)[/tex]:
[tex]\[ f(6) = 6^2 + 1 = 36 + 1 = 37 \][/tex]

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