Let ƒ(x)=x^2+3 and g(x)=-2x+6. Find each of the following. See Example 1. (ƒ+g)(3)

Key Concepts

Function Addition

Function addition involves combining two functions by adding their outputs for the same input. If ƒ(x) and g(x) are two functions, then (ƒ+g)(x) is defined as ƒ(x) + g(x). This concept is essential for solving problems that require evaluating the sum of two functions at a specific value.

Evaluating Functions

Evaluating functions means substituting a specific value into the function's expression to find the output. For example, to evaluate ƒ(3) for the function ƒ(x) = x^2 + 3, you would replace x with 3, resulting in ƒ(3) = 3^2 + 3 = 12. This skill is crucial for finding the values of functions at given points.

Composite Functions

While the question specifically asks for function addition, understanding composite functions is also important. A composite function is formed when one function is applied to the result of another function, denoted as (ƒ∘g)(x). Although not directly required here, recognizing the difference between addition and composition helps clarify function operations in algebra.