Question

find the domain and range of the function. $$ f(x)=-x $$

   find the domain and range of the function.

$$
f(x)=-x
$$

Calculus for AP

Calculus for AP

Jon Rogawski & Ray… 2nd Edition

Chapter 1, Problem 41

Instant Answer

Solved by Expert Linh Vu

03/03/2020

Step 1

In this case, the function is $f(x)=-x$. There are no restrictions on the value of x, as any real number can be substituted into the function. Therefore, the domain of the function is all real numbers, which can be written as $(-\infty, \infty)$. Show more…

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find the domain and range of the function. $$ f(x)=-x $$

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Key Concepts

Domain

The domain of a function is the complete set of possible input values for which the function is defined. This concept is crucial because it identifies all valid values that can be substituted into the function's rule without violating any mathematical restrictions, such as division by zero or taking the square root of a negative number when dealing with real numbers.

Range

The range of a function consists of all possible output values produced when the function is applied to every element in the domain. It is important to understand that the range may be a subset of the codomain, representing only those values the function can actually achieve through its operation on its domain.

Function

A function is a relation that uniquely associates each element of a set, known as the domain, with exactly one element of another set, the codomain. Understanding functions involves knowing how inputs are transformed into outputs according to a rule, which is essential when analyzing any mathematical relationship.

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