Math Problem Statement

Find the domain of the function f(x) = 7x^2 + 6x - 8. Write your answer in interval notation.

Solution

To find the domain of the function f(x)=7x2+6x8f(x) = 7x^2 + 6x - 8, we need to consider the types of values xx can take without causing issues in the expression. Here are the main steps to analyze this type of function:

  1. The function f(x)=7x2+6x8f(x) = 7x^2 + 6x - 8 is a polynomial.
  2. Polynomials are defined for all real values of xx because they do not contain any denominators, square roots, or logarithmic terms that could restrict their domain.

Thus, the domain of f(x)=7x2+6x8f(x) = 7x^2 + 6x - 8 is all real numbers.

In interval notation, the domain is: x(,)x \in (-\infty, \infty)

Would you like more details on polynomials and domains? Let me know if you have further questions.

Related Questions

  1. How do you find the domain of a rational function?
  2. What happens to the domain of a function if it includes a square root?
  3. How would the domain change if f(x)f(x) had a denominator?
  4. What are the steps to find the range of a quadratic function?
  5. Why are polynomials always defined for all real numbers?

Tip: For any polynomial function, the domain is always all real numbers because polynomials do not have restrictions like denominators or square roots.

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Math Problem Analysis

Mathematical Concepts

Algebra
Domain of a Function
Polynomials

Formulas

Polynomial functions are defined for all real numbers

Theorems

Domain of polynomial functions

Suitable Grade Level

Grades 9-10