High School

We appreciate your visit to Determine whether each of these functions f mathbb R to mathbb R is a one to one correspondence i e both onto and one to. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

Determine whether each of these functions \( f: \mathbb{R} \to \mathbb{R} \) is a one-to-one correspondence (i.e., both onto and one-to-one).

Answer :

Final answer:

The function f(x) described as a horizontal line is neither one-to-one nor onto, therefore it is not a one-to-one correspondence for any interval of x.

Explanation:

The question revolves around determining if a given function f(x), a mapping from real numbers to real numbers, is in fact a one-to-one correspondence, which means it must be both onto and one-to-one. We are given that f(x) is a horizontal line for the interval 0 ≤ x ≤ 20.

A horizontal line means the function has the same output for every input in the domain, thus, it cannot be one-to-one because different x values will have the same y value. Since it is not one-to-one, we can immediately conclude that it is not a one-to-one correspondence without even checking for it being onto. When graphing this function, it is clear that every x in the given interval maps to the same y, which does not cover all possible y values in the codomain of real numbers, further confirming it is not onto.

Thanks for taking the time to read Determine whether each of these functions f mathbb R to mathbb R is a one to one correspondence i e both onto and one to. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada