The function `f(x)=e^x+x ,` being differentiable and one-to-one, has a differentiable inverse `f^(-1)(x)dot` The value of `d/(dx)(f^(-1))` at the point `f(log2)` is (a)`1/(1n2)` (b) `1/3` (c) `1/4` (d) none of these

Options

A. `(1)/(In2)`
B. `(1)/(3)`
C. `(1)/(4)`
D. none of these

Explanation

To solve the problem, we need to find the value of \(\frac{d}{dx}(f^{-1}(x))\) at the point \(f(\log 2)\), where \(f(x) = e^x + x\).

### Step-by-Step Solution:

1. **Find the derivative of \(f(x)\)**:
\[ f(x) = e^x + x \]
...