If `g(x)=3x+2 and g(f(x))=x`, then f(2)=

Options

A. 0
B. 1
C. 2
D. 8

Explanation

To solve the problem, we need to find the value of \( f(2) \) given that \( g(x) = 3x + 2 \) and \( g(f(x)) = x \).

### Step-by-Step Solution:

1. **Understanding the equations**: We have two equations:
- \( g(x) = 3x + 2 \)
- \( g(f(x)) = x \)

2. **Substituting \( x = 2 \)**: We want to find \( f(2) \). To do this, we can substitute \( x = 2 \) into the second equation:
\[ g(f(2)) = 2 \]
This means that the output of \( g \) when we input \( f(2) \) should equal 2.

3. **Using the function \( g \)**: Now we can express \( g(f(2)) \) using the definition of \( g(x) \):
\[ g(f(2)) = 3(f(2)) + 2 \]
Setting this equal to 2 (from the previous step), we have:
\[ 3(f(2)) + 2 = 2 \]

4. **Solving for \( f(2) \)**: Now we solve the equation:
\[ 3(f(2)) + 2 = 2 \]
Subtract 2 from both sides:
\[ 3(f(2)) = 2 - 2 \]
Simplifying gives:
\[ 3(f(2)) = 0 \]
Now, divide both sides by 3:
\[ f(2) = 0 \]

5. **Final answer**: Therefore, the value of \( f(2) \) is:
\[ f(2) = 0 \]