Let `g, f:R rarr R` be defined by
`g(x)=(x+2)/(3), f(x)=3x-2`. Write fog (x)

Answer

To find the composition of the functions \( f \) and \( g \), denoted as \( f \circ g(x) \), we need to follow these steps:

1. **Identify the functions**:
- We have \( g(x) = \frac{x + 2}{3} \)
- We have \( f(x) = 3x - 2 \)

2. **Substitute \( g(x) \) into \( f(x) \)**:
- We need to find \( f(g(x)) \). This means we will substitute \( g(x) \) into \( f(x) \).
- So, we will replace \( x \) in \( f(x) \) with \( g(x) \):
\[ f(g(x)) = f\left(\frac{x + 2}{3}\right) \]

3. **Evaluate \( f \left( \frac{x + 2}{3} \right) \)**:
- Now, we will use the definition of \( f(x) \):
\[ f(t) = 3t - 2 \]
- Here, we let \( t = g(x) = \frac{x + 2}{3} \). Therefore:
\[ f\left(\frac{x + 2}{3}\right) = 3\left(\frac{x + 2}{3}\right) - 2 \]

4. **Simplify the expression**:
- Now, we simplify:
\[ f\left(\frac{x + 2}{3}\right) = \frac{3(x + 2)}{3} - 2 = (x + 2) - 2 \]
- This simplifies to:
\[ x + 2 - 2 = x \]

5. **Final result**:
- Therefore, the composition \( f \circ g(x) \) is:
\[ f \circ g(x) = x \]

### Final Answer:
\[ f \circ g(x) = x \]