Let `f(x)=x^(2)-4x-3, x gt2` and `g(x)` be the inverse of `f(x)`. Then the value `fo(g')`, where `f(x)=2`, is `"(here, g' represents the first derivative of g)"`

Answer

To solve the problem, we need to find the value of \( g'(5) \) where \( g(x) \) is the inverse function of \( f(x) = x^2 - 4x - 3 \) for \( x > 2 \), and we know that \( f(g(x)) = x \).

### Step-by-Step Solution:

1. **Identify the function**:
\[ f(x) = x^2 - 4x - 3 \]

2. **Find \( f(x) = 2 \)**:
We need to solve the equation:
\[ x^2 - 4x - 3 = 2 \]
Rearranging gives:
\[ x^2 - 4x - 5 = 0 \]

3. **Factor the quadratic**:
The equation can be factored as:
\[ (x - 5)(x + 1) = 0 \]
Thus, the solutions are:
\[ x = 5 \quad \text{or} \quad x = -1 \]

4. **Select the valid solution**:
Since \( x > 2 \), we take:
\[ x = 5 \]
Therefore, \( g(2) = 5 \).

5. **Differentiate the relationship**:
From the relationship \( g(f(x)) = x \), we differentiate both sides with respect to \( x \):
\[ g'(f(x)) \cdot f'(x) = 1 \]

6. **Find \( f'(x) \)**:
Differentiate \( f(x) \):
\[ f'(x) = 2x - 4 \]

7. **Evaluate \( f'(5) \)**:
Substitute \( x = 5 \) into \( f'(x) \):
\[ f'(5) = 2(5) - 4 = 10 - 4 = 6 \]

8. **Use the derivative relationship**:
Substitute \( x = 5 \) into the differentiated equation:
\[ g'(f(5)) \cdot f'(5) = 1 \]
Since \( f(5) = 2 \):
\[ g'(2) \cdot 6 = 1 \]

9. **Solve for \( g'(2) \)**:
\[ g'(2) = \frac{1}{6} \]

### Final Answer:
Thus, the value of \( g'(2) \) is:
\[ \boxed{\frac{1}{6}} \]