Answer :
We are given the functions
[tex]$$
f(x) = 3x^2 - 3x + 6 \quad \text{and} \quad g(x) = 2x.
$$[/tex]
To find [tex]$f(g(4))$[/tex], follow these steps:
1. First, evaluate [tex]$g(4)$[/tex]:
[tex]$$
g(4) = 2 \times 4 = 8.
$$[/tex]
2. Next, substitute [tex]$g(4)$[/tex] into [tex]$f(x)$[/tex] to compute [tex]$f(8)$[/tex]:
[tex]$$
f(8) = 3(8)^2 - 3(8) + 6.
$$[/tex]
3. Calculate each part:
[tex]$$
8^2 = 64,
$$[/tex]
so
[tex]$$
3(64) = 192,
$$[/tex]
and
[tex]$$
3(8) = 24.
$$[/tex]
4. Now, combine these results:
[tex]$$
f(8) = 192 - 24 + 6.
$$[/tex]
5. Finally, compute the sum:
[tex]$$
192 - 24 = 168,
$$[/tex]
and then
[tex]$$
168 + 6 = 174.
$$[/tex]
Thus, the value of [tex]$f(g(4))$[/tex] is [tex]$174$[/tex], which corresponds to option B.
[tex]$$
f(x) = 3x^2 - 3x + 6 \quad \text{and} \quad g(x) = 2x.
$$[/tex]
To find [tex]$f(g(4))$[/tex], follow these steps:
1. First, evaluate [tex]$g(4)$[/tex]:
[tex]$$
g(4) = 2 \times 4 = 8.
$$[/tex]
2. Next, substitute [tex]$g(4)$[/tex] into [tex]$f(x)$[/tex] to compute [tex]$f(8)$[/tex]:
[tex]$$
f(8) = 3(8)^2 - 3(8) + 6.
$$[/tex]
3. Calculate each part:
[tex]$$
8^2 = 64,
$$[/tex]
so
[tex]$$
3(64) = 192,
$$[/tex]
and
[tex]$$
3(8) = 24.
$$[/tex]
4. Now, combine these results:
[tex]$$
f(8) = 192 - 24 + 6.
$$[/tex]
5. Finally, compute the sum:
[tex]$$
192 - 24 = 168,
$$[/tex]
and then
[tex]$$
168 + 6 = 174.
$$[/tex]
Thus, the value of [tex]$f(g(4))$[/tex] is [tex]$174$[/tex], which corresponds to option B.
