Answer :
To find [tex]\( f(g(4)) \)[/tex], we need to follow two main steps.
1. Calculate [tex]\( g(4) \)[/tex]:
The function [tex]\( g(x) \)[/tex] is given as [tex]\( g(x) = 2x \)[/tex]. To find [tex]\( g(4) \)[/tex], substitute 4 into the function:
[tex]\[
g(4) = 2 \times 4 = 8
\][/tex]
2. Calculate [tex]\( f(g(4)) = f(8) \)[/tex]:
Now that we know [tex]\( g(4) = 8 \)[/tex], we substitute 8 into the function [tex]\( f(x) = 3x^2 - 3x + 6 \)[/tex]:
[tex]\[
f(8) = 3(8)^2 - 3(8) + 6
\][/tex]
First, calculate [tex]\( 8^2 \)[/tex]:
[tex]\[
8^2 = 64
\][/tex]
Then, plug it into the equation:
[tex]\[
f(8) = 3(64) - 3(8) + 6
\][/tex]
Calculate the terms separately:
[tex]\[
3 \times 64 = 192
\][/tex]
[tex]\[
3 \times 8 = 24
\][/tex]
Substitute these values back into the equation:
[tex]\[
f(8) = 192 - 24 + 6
\][/tex]
Now, perform the addition and subtraction:
[tex]\[
192 - 24 = 168
\][/tex]
[tex]\[
168 + 6 = 174
\][/tex]
Hence, the value of [tex]\( f(g(4)) \)[/tex] is [tex]\(\boxed{174}\)[/tex].
1. Calculate [tex]\( g(4) \)[/tex]:
The function [tex]\( g(x) \)[/tex] is given as [tex]\( g(x) = 2x \)[/tex]. To find [tex]\( g(4) \)[/tex], substitute 4 into the function:
[tex]\[
g(4) = 2 \times 4 = 8
\][/tex]
2. Calculate [tex]\( f(g(4)) = f(8) \)[/tex]:
Now that we know [tex]\( g(4) = 8 \)[/tex], we substitute 8 into the function [tex]\( f(x) = 3x^2 - 3x + 6 \)[/tex]:
[tex]\[
f(8) = 3(8)^2 - 3(8) + 6
\][/tex]
First, calculate [tex]\( 8^2 \)[/tex]:
[tex]\[
8^2 = 64
\][/tex]
Then, plug it into the equation:
[tex]\[
f(8) = 3(64) - 3(8) + 6
\][/tex]
Calculate the terms separately:
[tex]\[
3 \times 64 = 192
\][/tex]
[tex]\[
3 \times 8 = 24
\][/tex]
Substitute these values back into the equation:
[tex]\[
f(8) = 192 - 24 + 6
\][/tex]
Now, perform the addition and subtraction:
[tex]\[
192 - 24 = 168
\][/tex]
[tex]\[
168 + 6 = 174
\][/tex]
Hence, the value of [tex]\( f(g(4)) \)[/tex] is [tex]\(\boxed{174}\)[/tex].
