Question

3.6 graphs of functions (homework) score: 5/17 answered: 5/17 question 6 find the domain of the function f(x) = 7x² - 5x - 10. the domain is x ∈ question help: video written example submit question jump to answer

Explanation:

Step1: Identify the function type

The function \( f(x) = 7x^2 - 5x - 10 \) is a polynomial function (specifically a quadratic function, since the highest power of \( x \) is 2).

Step2: Recall the domain of polynomial functions

For any polynomial function (including linear, quadratic, cubic, etc.), the domain is all real numbers. This is because there are no restrictions on the input \( x \) (such as division by zero or taking the square root of a negative number) that would exclude any real number from being a valid input. So, the domain of \( f(x) \) is all real numbers. In interval notation, this is \( (-\infty, \infty) \), and in set - builder notation, it can be written as \( \{x|x\in\mathbb{R}\} \) or simply stated as all real numbers.

Answer:

The domain is \( x\in (-\infty, \infty) \) (or equivalently, all real numbers).