To find the value of [tex]\( f(g(1)) \)[/tex], we need to follow the steps below:
1. Evaluate [tex]\( g(1) \)[/tex]:
We are given that [tex]\( g(x) = x \)[/tex]. Therefore, [tex]\( g(1) = 1 \)[/tex].
2. Substitute [tex]\( g(1) \)[/tex] into [tex]\( f(x) \)[/tex]:
Now that we have [tex]\( g(1) = 1 \)[/tex], we will substitute this into the function [tex]\( f(x) \)[/tex].
[tex]\[
f(g(1)) = f(1)
\][/tex]
3. Calculate [tex]\( f(1) \)[/tex]:
The function [tex]\( f(x) \)[/tex] is given by [tex]\( f(x) = 3 \sqrt{x} + 1 \)[/tex]. We need to evaluate it at [tex]\( x = 1 \)[/tex].
[tex]\[
f(1) = 3 \sqrt{1} + 1
\][/tex]
Simplifying, we get:
[tex]\[
f(1) = 3 \times 1 + 1 = 4
\][/tex]
So, the value of [tex]\( f(g(1)) \)[/tex] is [tex]\( 4.0 \)[/tex].
Therefore, none of the options A, B, or C are correct. The correct answer is [tex]\( 4.0 \)[/tex].
