Answer :
To find [tex]\(f(g(4))\)[/tex], we need to use the given functions [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex].
1. First, let's evaluate [tex]\(g(4)\)[/tex]. The function [tex]\(g(x) = 2x\)[/tex]. By substituting 4 into the function:
[tex]\[
g(4) = 2 \times 4 = 8
\][/tex]
2. Next, we use the result from [tex]\(g(4)\)[/tex] to find [tex]\(f(g(4))\)[/tex], which is the same as [tex]\(f(8)\)[/tex]. The function [tex]\(f(x) = 3x^2 - 3x + 6\)[/tex]. By substituting 8 into the function:
[tex]\[
f(8) = 3(8)^2 - 3(8) + 6
\][/tex]
3. Calculate each term:
- [tex]\(3(8)^2 = 3 \times 64 = 192\)[/tex]
- [tex]\(-3(8) = -24\)[/tex]
- The constant term is [tex]\(+6\)[/tex]
4. Add all the terms together:
[tex]\[
f(8) = 192 - 24 + 6 = 174
\][/tex]
So, the value of [tex]\(f(g(4))\)[/tex] is 174. Therefore, the correct answer is C) 174.
1. First, let's evaluate [tex]\(g(4)\)[/tex]. The function [tex]\(g(x) = 2x\)[/tex]. By substituting 4 into the function:
[tex]\[
g(4) = 2 \times 4 = 8
\][/tex]
2. Next, we use the result from [tex]\(g(4)\)[/tex] to find [tex]\(f(g(4))\)[/tex], which is the same as [tex]\(f(8)\)[/tex]. The function [tex]\(f(x) = 3x^2 - 3x + 6\)[/tex]. By substituting 8 into the function:
[tex]\[
f(8) = 3(8)^2 - 3(8) + 6
\][/tex]
3. Calculate each term:
- [tex]\(3(8)^2 = 3 \times 64 = 192\)[/tex]
- [tex]\(-3(8) = -24\)[/tex]
- The constant term is [tex]\(+6\)[/tex]
4. Add all the terms together:
[tex]\[
f(8) = 192 - 24 + 6 = 174
\][/tex]
So, the value of [tex]\(f(g(4))\)[/tex] is 174. Therefore, the correct answer is C) 174.
