Answer :
To solve for [tex]\( f(g(4)) \)[/tex], we need to evaluate the functions [tex]\( g(x) \)[/tex] and [tex]\( f(x) \)[/tex].
1. Evaluate [tex]\( g(4) \)[/tex]:
The function [tex]\( g(x) \)[/tex] is given by:
[tex]\[
g(x) = 3x - 5
\][/tex]
Substitute [tex]\( x = 4 \)[/tex] into the function:
[tex]\[
g(4) = 3(4) - 5 = 12 - 5 = 7
\][/tex]
2. Evaluate [tex]\( f(g(4)) = f(7) \)[/tex]:
Now, we need to use the result from [tex]\( g(4) \)[/tex] to find [tex]\( f(7) \)[/tex]. The function [tex]\( f(x) \)[/tex] is given by:
[tex]\[
f(x) = (x + 1)^2
\][/tex]
Substitute [tex]\( x = 7 \)[/tex] into the function:
[tex]\[
f(7) = (7 + 1)^2 = 8^2 = 64
\][/tex]
Therefore, the value of [tex]\( f(g(4)) \)[/tex] is [tex]\( 64 \)[/tex].
1. Evaluate [tex]\( g(4) \)[/tex]:
The function [tex]\( g(x) \)[/tex] is given by:
[tex]\[
g(x) = 3x - 5
\][/tex]
Substitute [tex]\( x = 4 \)[/tex] into the function:
[tex]\[
g(4) = 3(4) - 5 = 12 - 5 = 7
\][/tex]
2. Evaluate [tex]\( f(g(4)) = f(7) \)[/tex]:
Now, we need to use the result from [tex]\( g(4) \)[/tex] to find [tex]\( f(7) \)[/tex]. The function [tex]\( f(x) \)[/tex] is given by:
[tex]\[
f(x) = (x + 1)^2
\][/tex]
Substitute [tex]\( x = 7 \)[/tex] into the function:
[tex]\[
f(7) = (7 + 1)^2 = 8^2 = 64
\][/tex]
Therefore, the value of [tex]\( f(g(4)) \)[/tex] is [tex]\( 64 \)[/tex].
