Answer :
To solve the problem and find the value of [tex]\( f(g(4)) \)[/tex], we need to follow these steps:
1. Evaluate [tex]\( g(4) \)[/tex]:
Given the function [tex]\( g(x) = 2x \)[/tex], we substitute [tex]\( x = 4 \)[/tex] to find [tex]\( g(4) \)[/tex].
[tex]\[
g(4) = 2 \times 4 = 8
\][/tex]
2. Evaluate [tex]\( f(g(4)) \)[/tex]:
We have found that [tex]\( g(4) = 8 \)[/tex]. Now, we need to find [tex]\( f(8) \)[/tex] using the function [tex]\( f(x) = 3x^2 - 3x + 6 \)[/tex].
Substitute [tex]\( x = 8 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[
f(8) = 3 \times 8^2 - 3 \times 8 + 6
\][/tex]
Calculate each term step by step:
- [tex]\( 8^2 = 64 \)[/tex]
- [tex]\( 3 \times 64 = 192 \)[/tex]
- [tex]\( 3 \times 8 = 24 \)[/tex]
Substituting back, we have:
[tex]\[
f(8) = 192 - 24 + 6
\][/tex]
Simplify:
[tex]\[
f(8) = 168 + 6 = 174
\][/tex]
Therefore, the value of [tex]\( f(g(4)) \)[/tex] is [tex]\( 174 \)[/tex]. The correct option is A) 174.
1. Evaluate [tex]\( g(4) \)[/tex]:
Given the function [tex]\( g(x) = 2x \)[/tex], we substitute [tex]\( x = 4 \)[/tex] to find [tex]\( g(4) \)[/tex].
[tex]\[
g(4) = 2 \times 4 = 8
\][/tex]
2. Evaluate [tex]\( f(g(4)) \)[/tex]:
We have found that [tex]\( g(4) = 8 \)[/tex]. Now, we need to find [tex]\( f(8) \)[/tex] using the function [tex]\( f(x) = 3x^2 - 3x + 6 \)[/tex].
Substitute [tex]\( x = 8 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[
f(8) = 3 \times 8^2 - 3 \times 8 + 6
\][/tex]
Calculate each term step by step:
- [tex]\( 8^2 = 64 \)[/tex]
- [tex]\( 3 \times 64 = 192 \)[/tex]
- [tex]\( 3 \times 8 = 24 \)[/tex]
Substituting back, we have:
[tex]\[
f(8) = 192 - 24 + 6
\][/tex]
Simplify:
[tex]\[
f(8) = 168 + 6 = 174
\][/tex]
Therefore, the value of [tex]\( f(g(4)) \)[/tex] is [tex]\( 174 \)[/tex]. The correct option is A) 174.
