Math Problem Statement

g(x) = 

x2 − 3x − 18, find domain in interval notation

Solution

To find the domain of the function g(x)=x23x18g(x) = x^2 - 3x - 18, we need to determine the set of all possible values of xx for which the function is defined.

Since g(x)g(x) is a polynomial function, it is defined for all real numbers. There are no restrictions (like division by zero or taking the square root of a negative number) that would limit the domain.

Thus, the domain of g(x)g(x) is all real numbers.

In interval notation, the domain is:

Domain of g(x): (,)\text{Domain of } g(x): \ (-\infty, \infty)

Would you like more details or have any questions?

Here are 5 related questions:

  1. How would you find the domain of a function that includes a square root?
  2. What is the range of the function g(x)=x23x18g(x) = x^2 - 3x - 18?
  3. How do you find the vertex of the quadratic function g(x)=x23x18g(x) = x^2 - 3x - 18?
  4. Can the function g(x)=x23x18g(x) = x^2 - 3x - 18 have any restrictions if it is part of a composite function?
  5. How does the domain of a polynomial function generally compare to other types of functions?

Tip: When working with quadratic functions, always check if there are any real restrictions like square roots or denominators to determine the domain correctly.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Polynomial Functions
Domain and Range

Formulas

General form of a quadratic equation: ax^2 + bx + c

Theorems

Properties of polynomial functions

Suitable Grade Level

Grades 9-10