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Consider the function f: R → R given by f(x) = (e^(|x|) - e^(-x))/(e^x + e^(-x)). Which of the following is true?

1. f is injective as well as surjective
2. f is injective but not surjective
3. f is surjective but not injective
4. f is neither injective nor surjective

Correct answer: f is neither injective nor surjective

Solution

The function f is neither injective nor surjective because it does not produce unique outputs for every input (indicating it is not injective) and it does not cover all possible real numbers as outputs (indicating it is not surjective).

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