Question

Let \( f : \mathbb{R} \to \mathbb{R} \) be a function defined by \( f(x) = \frac{e^{|x|} - e^{-x}}{e^x + e^{-x}} \), then \( f \) is:

• A. One-one and onto.
• B. One-one but not onto.
• C. Onto but not one-one.
• D. Neither onto nor one-one.

Hint:

To determine whether a function is one-to-one, check if it is either strictly increasing or strictly decreasing. To check if it is onto, determine if the function can take all possible values in the codomain.

Answer 1

The Correct Option is B