Let's determine the value of [tex]\( f(g(3)) \)[/tex] step-by-step by first evaluating [tex]\( g(3) \)[/tex], and then substituting that result into the function [tex]\( f(x) \)[/tex].
1. Evaluate [tex]\( g(3) \)[/tex]:
[tex]\[
g(x) = \frac{x+1}{x-1}
\][/tex]
Substitute [tex]\( x = 3 \)[/tex]:
[tex]\[
g(3) = \frac{3 + 1}{3 - 1} = \frac{4}{2} = 2
\][/tex]
2. Evaluate [tex]\( f(g(3)) \)[/tex]:
From the previous step, we know [tex]\( g(3) = 2 \)[/tex]. Now, we need to find [tex]\( f(2) \)[/tex]:
[tex]\[
f(x) = 3x - 7
\][/tex]
Substitute [tex]\( x = 2 \)[/tex]:
[tex]\[
f(2) = 3 \cdot 2 - 7 = 6 - 7 = -1
\][/tex]
So, the value of [tex]\( f(g(3)) \)[/tex] is [tex]\( -1 \)[/tex].
Thus, the correct answer is:
A. -1
