For the pair of functions defined, find (ƒ-g)(x). Give the domain of each. See Example 2. ƒ(x)=2x^2-3x, g(x)=x^2-x+3

Key Concepts

Function Subtraction

Function subtraction involves taking two functions, ƒ(x) and g(x), and creating a new function (ƒ-g)(x) by subtracting the output of g(x) from ƒ(x) for each x in the domain. This operation is defined as (ƒ-g)(x) = ƒ(x) - g(x). Understanding this concept is crucial for combining functions and analyzing their behavior.

Domain of a Function

The domain of a function is the set of all possible input values (x-values) for which the function is defined. For polynomial functions like ƒ(x) and g(x), the domain is typically all real numbers, as polynomials do not have restrictions such as division by zero or square roots of negative numbers. Identifying the domain is essential for understanding where the function operates.

Polynomial Functions

Polynomial functions are mathematical expressions that involve variables raised to whole number powers, combined using addition, subtraction, and multiplication. In this case, both ƒ(x) = 2x² - 3x and g(x) = x² - x + 3 are polynomials. Recognizing the characteristics of polynomial functions, such as their continuity and smoothness, is important for analyzing their graphs and behaviors.