Let `f: R to R ` be defined as `f(x) = e^("sgn "x)+ e^(x^(2))`. Then find the range of the function, and also indentify the type of the function : one-one or many-one.

Explanation

To solve the problem, we need to analyze the function \( f(x) = e^{\text{sgn}(x)} + e^{x^2} \) and find its range, as well as determine if it is a one-one or many-one function.

### Step 1: Understand the Signum Function
The signum function, denoted as \( \text{sgn}(x) \), is defined as follows:
- \( \text{sgn}(x) = -1 \) if \( x < 0 \)
- \( \text{sgn}(x) = 0 \) if \( x = 0 \)
- \( \text{sgn}(x) = 1 \) if \( x > 0 \)

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