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 Addition

Function addition involves combining two functions by adding their outputs for each input value. For functions ƒ(x) and g(x), the sum (ƒ+g)(x) is calculated as ƒ(x) + g(x). This operation is fundamental in algebra as it allows for the creation of new functions from existing ones, facilitating further analysis and manipulation.

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) = 2x² - 3x and g(x) = x² - x + 3, the domain is typically all real numbers, as polynomials do not have restrictions such as division by zero or square roots of negative numbers.

Polynomial Functions

Polynomial functions are mathematical expressions that involve variables raised to whole number powers, combined using addition, subtraction, and multiplication. The functions given, ƒ(x) = 2x² - 3x and g(x) = x² - x + 3, are both polynomials of degree 2. Understanding their structure is crucial for performing operations like addition and analyzing their behavior.