Answer :
To solve the problem of evaluating [tex]\( f(g(2)) \)[/tex] given the functions [tex]\( f(x) = 3x^2 - 7 \)[/tex] and [tex]\( g(x) = x^3 + 1 \)[/tex], we will follow these steps:
1. Evaluate [tex]\( g(2) \)[/tex]:
First, we need to find [tex]\( g(2) \)[/tex]. The function [tex]\( g(x) = x^3 + 1 \)[/tex]. Substituting [tex]\( x = 2 \)[/tex] into this function gives us:
[tex]\[
g(2) = 2^3 + 1
\][/tex]
Calculate [tex]\( 2^3 \)[/tex], which is:
[tex]\[
2^3 = 8
\][/tex]
Add 1 to 8:
[tex]\[
8 + 1 = 9
\][/tex]
So, [tex]\( g(2) = 9 \)[/tex].
2. Substitute [tex]\( g(2) \)[/tex] in [tex]\( f(x) \)[/tex]:
Now that we know [tex]\( g(2) = 9 \)[/tex], we substitute this value into the function [tex]\( f(x) \)[/tex].
The function given is [tex]\( f(x) = 3x^2 - 7 \)[/tex]. We replace [tex]\( x \)[/tex] with 9:
[tex]\[
f(9) = 3(9^2) - 7
\][/tex]
Calculate [tex]\( 9^2 \)[/tex], which is:
[tex]\[
9^2 = 81
\][/tex]
Multiply 81 by 3:
[tex]\[
3 \times 81 = 243
\][/tex]
Subtract 7 from 243:
[tex]\[
243 - 7 = 236
\][/tex]
Thus, [tex]\( f(g(2)) = f(9) = 236 \)[/tex].
Therefore, the value of [tex]\( f(g(2)) \)[/tex] is 236.
1. Evaluate [tex]\( g(2) \)[/tex]:
First, we need to find [tex]\( g(2) \)[/tex]. The function [tex]\( g(x) = x^3 + 1 \)[/tex]. Substituting [tex]\( x = 2 \)[/tex] into this function gives us:
[tex]\[
g(2) = 2^3 + 1
\][/tex]
Calculate [tex]\( 2^3 \)[/tex], which is:
[tex]\[
2^3 = 8
\][/tex]
Add 1 to 8:
[tex]\[
8 + 1 = 9
\][/tex]
So, [tex]\( g(2) = 9 \)[/tex].
2. Substitute [tex]\( g(2) \)[/tex] in [tex]\( f(x) \)[/tex]:
Now that we know [tex]\( g(2) = 9 \)[/tex], we substitute this value into the function [tex]\( f(x) \)[/tex].
The function given is [tex]\( f(x) = 3x^2 - 7 \)[/tex]. We replace [tex]\( x \)[/tex] with 9:
[tex]\[
f(9) = 3(9^2) - 7
\][/tex]
Calculate [tex]\( 9^2 \)[/tex], which is:
[tex]\[
9^2 = 81
\][/tex]
Multiply 81 by 3:
[tex]\[
3 \times 81 = 243
\][/tex]
Subtract 7 from 243:
[tex]\[
243 - 7 = 236
\][/tex]
Thus, [tex]\( f(g(2)) = f(9) = 236 \)[/tex].
Therefore, the value of [tex]\( f(g(2)) \)[/tex] is 236.
