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Answer :
To evaluate [tex]\( f(g(2)) \)[/tex], we need to follow these steps:
1. Evaluate [tex]\( g(2) \)[/tex]:
- The function [tex]\( g(x) \)[/tex] is [tex]\( x^3 + 1 \)[/tex].
- Substitute 2 for [tex]\( x \)[/tex] in the function [tex]\( g(x) \)[/tex]:
[tex]\[
g(2) = 2^3 + 1 = 8 + 1 = 9
\][/tex]
2. Evaluate [tex]\( f(g(2)) \)[/tex] or [tex]\( f(9) \)[/tex]:
- Now that we know [tex]\( g(2) = 9 \)[/tex], we substitute 9 into the function [tex]\( f(x) \)[/tex].
- The function [tex]\( f(x) \)[/tex] is [tex]\( 3x^2 - 7 \)[/tex].
- Substitute 9 for [tex]\( x \)[/tex] in the function [tex]\( f(x) \)[/tex]:
[tex]\[
f(9) = 3(9)^2 - 7 = 3(81) - 7 = 243 - 7 = 236
\][/tex]
Thus, the value of [tex]\( f(g(2)) \)[/tex] is 236. Therefore, the correct answer is 236.
1. Evaluate [tex]\( g(2) \)[/tex]:
- The function [tex]\( g(x) \)[/tex] is [tex]\( x^3 + 1 \)[/tex].
- Substitute 2 for [tex]\( x \)[/tex] in the function [tex]\( g(x) \)[/tex]:
[tex]\[
g(2) = 2^3 + 1 = 8 + 1 = 9
\][/tex]
2. Evaluate [tex]\( f(g(2)) \)[/tex] or [tex]\( f(9) \)[/tex]:
- Now that we know [tex]\( g(2) = 9 \)[/tex], we substitute 9 into the function [tex]\( f(x) \)[/tex].
- The function [tex]\( f(x) \)[/tex] is [tex]\( 3x^2 - 7 \)[/tex].
- Substitute 9 for [tex]\( x \)[/tex] in the function [tex]\( f(x) \)[/tex]:
[tex]\[
f(9) = 3(9)^2 - 7 = 3(81) - 7 = 243 - 7 = 236
\][/tex]
Thus, the value of [tex]\( f(g(2)) \)[/tex] is 236. Therefore, the correct answer is 236.
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