Is the pair of the functions `e^(sqrt(log_(e)x))` and `sqrt(x)` identical ?

Explanation

To determine if the functions \( f(x) = e^{\sqrt{\log_e x}} \) and \( g(x) = \sqrt{x} \) are identical, we need to check three conditions:

1. **Equal Domains**: Both functions must be defined for the same set of \( x \) values.
2. **Equal Ranges**: Both functions must produce the same set of output values for their respective domains.
3. **Equal Values for All Inputs in the Domain**: For every \( x \) in the domain, \( f(x) \) must equal \( g(x) \).

### Step 1: Determine the Domain of \( f(x) = e^{\sqrt{\log_e x}} \)

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