Let `I` be an interval disjointed from `[-1,\ 1]` . Prove that the function `f(x)=x+1/x` is increasing on `I` .

Explanation

To prove that the function \( f(x) = x + \frac{1}{x} \) is increasing on the interval \( I \) which is disjoint from \([-1, 1]\), we will follow these steps:

### Step 1: Find the derivative of the function
To determine if \( f(x) \) is increasing, we first need to find its derivative \( f'(x) \).

\[ f(x) = x + \frac{1}{x} \]
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