https://file.aiquickdraw.com/mathbot/file/1727004502331v21nn93j.jpg

We are given two functions:

\[
f(x) = 3x - 5
\]
\[
g(x) = \frac{4x - 2}{6 - 4x}, \quad \text{with } x \neq \frac{3}{2}
\]

We need to find the value of \((g \circ f)(2)\), which represents the composition of \(g\) and \(f\) evaluated at \(x = 2\).

### Step 1: Find \(f(2)\)
First, we substitute \(x = 2\) into the function \(f(x)\):

\[
f(2) = 3(2) - 5 = 6 - 5 = 1
\]

### Step 2: Find \(g(f(2)) = g(1)\)
Now that we know \(f(2) = 1\), we substitute this value into the function \(g(x)\):

\[
g(1) = \frac{4(1) - 2}{6 - 4(1)} = \frac{4 - 2}{6 - 4} = \frac{2}{2} = 1
\]

Thus, the value of \((g \circ f)(2)\) is \(1\).

The correct answer is:
\[
\boxed{d. 1}
\]

Would you like further explanation or have any other questions?

### Related Questions:
1. What is the domain of the composite function \(g \circ f\)?
2. If \(f(x) = 2x - 4\), how would the composite function change?
3. What happens if \(x = \frac{3}{2}\)? Why is it excluded?
4. Can we always compose two functions, or are there restrictions?
5. How can the composition of functions be applied to real-world problems?

### Tip:
When evaluating composite functions, always work from the inside out, starting with the innermost function.

Diketahui fungsi f(x) = 3x - 5 dan g(x) = (4x - 2) / (6 - 4x). Nilai komposisi fungsi (g o f)(2) adalah?

Learn how to find the value of the function composition (g o f)(2) where f(x) = 3x - 5 and g(x) = (4x - 2) / (6 - 4x). This problem covers key algebraic concepts in function composition. Suitable for high school students in Grades 10-12.

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