Answer :
We want to find the value of
[tex]$$
f(g(4)).
$$[/tex]
Step 1: Compute [tex]\( g(4) \)[/tex].
The function [tex]\( g(x) \)[/tex] is defined as:
[tex]$$
g(x) = 2x.
$$[/tex]
So, we have:
[tex]$$
g(4) = 2 \cdot 4 = 8.
$$[/tex]
Step 2: Compute [tex]\( f(g(4)) \)[/tex] by evaluating [tex]\( f(8) \)[/tex].
The function [tex]\( f(x) \)[/tex] is given by:
[tex]$$
f(x) = 3x^2 - 3x + 6.
$$[/tex]
Substitute [tex]\( x = 8 \)[/tex] into [tex]\( f(x) \)[/tex]:
[tex]$$
f(8) = 3(8)^2 - 3(8) + 6.
$$[/tex]
Step 3: Simplify [tex]\( f(8) \)[/tex].
First, calculate [tex]\( (8)^2 \)[/tex]:
[tex]$$
8^2 = 64.
$$[/tex]
Then substitute:
[tex]$$
f(8) = 3 \cdot 64 - 24 + 6 = 192 - 24 + 6.
$$[/tex]
Now, combine the terms:
[tex]$$
192 - 24 = 168,
$$[/tex]
and then:
[tex]$$
168 + 6 = 174.
$$[/tex]
Thus, the final result is:
[tex]$$
f(g(4)) = 174.
$$[/tex]
The correct answer is 174.
[tex]$$
f(g(4)).
$$[/tex]
Step 1: Compute [tex]\( g(4) \)[/tex].
The function [tex]\( g(x) \)[/tex] is defined as:
[tex]$$
g(x) = 2x.
$$[/tex]
So, we have:
[tex]$$
g(4) = 2 \cdot 4 = 8.
$$[/tex]
Step 2: Compute [tex]\( f(g(4)) \)[/tex] by evaluating [tex]\( f(8) \)[/tex].
The function [tex]\( f(x) \)[/tex] is given by:
[tex]$$
f(x) = 3x^2 - 3x + 6.
$$[/tex]
Substitute [tex]\( x = 8 \)[/tex] into [tex]\( f(x) \)[/tex]:
[tex]$$
f(8) = 3(8)^2 - 3(8) + 6.
$$[/tex]
Step 3: Simplify [tex]\( f(8) \)[/tex].
First, calculate [tex]\( (8)^2 \)[/tex]:
[tex]$$
8^2 = 64.
$$[/tex]
Then substitute:
[tex]$$
f(8) = 3 \cdot 64 - 24 + 6 = 192 - 24 + 6.
$$[/tex]
Now, combine the terms:
[tex]$$
192 - 24 = 168,
$$[/tex]
and then:
[tex]$$
168 + 6 = 174.
$$[/tex]
Thus, the final result is:
[tex]$$
f(g(4)) = 174.
$$[/tex]
The correct answer is 174.
