Find fog if `f(x)= x-2 ` and `g(x) = 3x`

Explanation

To find \( f \circ g \) (denoted as \( fog \)), we need to follow these steps:

1. **Identify the functions**: We have two functions given:
- \( f(x) = x - 2 \)
- \( g(x) = 3x \)

2. **Understand the notation \( f \circ g \)**: The notation \( f \circ g \) means we need to find \( f(g(x)) \). This means we will take the output of \( g(x) \) and use it as the input for \( f(x) \).

3. **Calculate \( g(x) \)**:
\[ g(x) = 3x \]

4. **Substitute \( g(x) \) into \( f(x) \)**: Now we need to find \( f(g(x)) \), which is \( f(3x) \).
\[ f(g(x)) = f(3x) \]

5. **Use the function \( f(x) \)**: Substitute \( 3x \) into the function \( f(x) \):
\[ f(3x) = 3x - 2 \]

6. **Final result**: Therefore, \( f \circ g = f(g(x)) = 3x - 2 \).

So, the final answer is:
\[ f \circ g = 3x - 2 \]