Define the function f: R -> (0, 1], where f(x) = e^(-x^2). Is this map surjective only, injective only, bijective, or none of these options?

Question

Define the function f: R -> (0, 1], where f(x) = e^(-x^2). Is this map surjective only, injective only, bijective, or none of these options?
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Solution 1

The function f is neither surjective, injective, nor bijective.

Here's why:

  1. Surjectivity: A function is surjective (or onto) if for every element in the codomain, there is at least one element in the domain that maps to it. In this case, the codomain is the interval (0, 1]. However, not every e Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solv

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