Given:
[tex]\[ f(x) = x^2 + 1 \][/tex]
[tex]\[ g(x) = x - 4 \][/tex]

Which value is equivalent to [tex]\((f \circ g)(10)\)[/tex]?



Answer :

To determine the value of [tex]\((f \circ g)(10)\)[/tex], we need to follow these steps:

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

2. Calculate [tex]\( g(10) \)[/tex]:
- Substitute [tex]\( x = 10 \)[/tex] into the function [tex]\( g \)[/tex]:
[tex]\[ g(10) = 10 - 4 = 6 \][/tex]

3. Calculate [tex]\( f(g(10)) \)[/tex]:
- We found that [tex]\( g(10) = 6 \)[/tex] in the previous step.
- Now, substitute [tex]\( x = 6 \)[/tex] into the function [tex]\( f \)[/tex]:
[tex]\[ f(6) = 6^2 + 1 = 36 + 1 = 37 \][/tex]

Therefore, the value of [tex]\((f \circ g)(10)\)[/tex] is [tex]\( f(g(10)) \)[/tex], which is [tex]\( 37 \)[/tex]. So, the equivalent value is:
[tex]\[ (f \circ g)(10) = 37 \][/tex]