Question

Determine whether each function is a one-to-one function. $y=x^{2}-9, x \geq 0$

Name: Problem 33, Chapter 9: Intermediate Algebra for College Students
Uploaded: 2020-04-02T23:26:23-08:00
Duration: 34 s
Channel: Linh Vu
Description: Determine whether each function is a one-to-one function. y=x^2-9, x ≥0

   Determine whether each function is a one-to-one function.
$y=x^{2}-9, x \geq 0$

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 9, Problem 33

Instant Answer

Solved by Expert Linh Vu

04/02/2020

Step 1

A one-to-one function (also called an injective function) is a function where each input has a unique output, and each output has a unique input. In other words, no two different inputs produce the same output. Show more…

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Determine whether each function is a one-to-one function. $y=x^{2}-9, x \geq 0$

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Key Concepts

One-to-one Function

A one-to-one function is defined as a function in which each value in the range is produced by exactly one input from the domain. In other words, if f(a) = f(b) then a must equal b, ensuring that no two distinct inputs have the same output.

Horizontal Line Test

The horizontal line test is a graphical method used to determine if a function is one-to-one. If every horizontal line intersects the graph of the function at most once, then the function passes the test and is one-to-one.

Domain Restriction

Domain restriction is the process of limiting the set of input values for a function, which can alter properties like one-to-one behavior. Restricting the domain can often transform a non-one-to-one function into a one-to-one function by preventing multiple inputs from producing the same output.

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