Let `f:R to R` be defined by `f(x) =e^(x)-e^(-x).` Prove that `f(x)` is invertible. Also find the inverse function.

Explanation

To prove that the function \( f(x) = e^x - e^{-x} \) is invertible and to find its inverse, we will follow these steps:

### Step 1: Prove that \( f(x) \) is one-to-one (injective)

To prove that \( f(x) \) is one-to-one, we need to show that if \( f(p) = f(q) \), then \( p = q \).

Assume \( f(p) = f(q) \):
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