Answer :
To solve the problem, we need to compute the value of [tex]\( f(g(4)) \)[/tex].
Step 1: Compute [tex]\( g(4) \)[/tex].
The function [tex]\( g(x) \)[/tex] is given by:
[tex]$$
g(x) = 3x - 5.
$$[/tex]
Replacing [tex]\( x \)[/tex] with 4:
[tex]$$
g(4) = 3 \times 4 - 5 = 12 - 5 = 7.
$$[/tex]
Step 2: Compute [tex]\( f(g(4)) \)[/tex], which is [tex]\( f(7) \)[/tex].
The function [tex]\( f(x) \)[/tex] is given by:
[tex]$$
f(x) = (x+1)^2.
$$[/tex]
Now substitute [tex]\( x = 7 \)[/tex]:
[tex]$$
f(7) = (7+1)^2 = 8^2 = 64.
$$[/tex]
Thus, the final answer is [tex]\( \boxed{64} \)[/tex].
Step 1: Compute [tex]\( g(4) \)[/tex].
The function [tex]\( g(x) \)[/tex] is given by:
[tex]$$
g(x) = 3x - 5.
$$[/tex]
Replacing [tex]\( x \)[/tex] with 4:
[tex]$$
g(4) = 3 \times 4 - 5 = 12 - 5 = 7.
$$[/tex]
Step 2: Compute [tex]\( f(g(4)) \)[/tex], which is [tex]\( f(7) \)[/tex].
The function [tex]\( f(x) \)[/tex] is given by:
[tex]$$
f(x) = (x+1)^2.
$$[/tex]
Now substitute [tex]\( x = 7 \)[/tex]:
[tex]$$
f(7) = (7+1)^2 = 8^2 = 64.
$$[/tex]
Thus, the final answer is [tex]\( \boxed{64} \)[/tex].
