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

Key Concepts

Function Notation

Function notation is a way to represent mathematical functions in a clear and concise manner. In this context, ƒ(x) and g(x) denote two different functions, where ƒ(x) = x² + 3 and g(x) = -2x + 6. Understanding how to read and interpret these notations is essential for performing operations on the functions.

Function Operations

Function operations involve combining two or more functions through addition, subtraction, multiplication, or division. In this case, (ƒ - g)(x) represents the subtraction of function g from function ƒ. This operation requires substituting the expressions of both functions and simplifying the result to find the new function.

Evaluating Functions

Evaluating functions means substituting a specific value into the function's expression to find the output. For example, to find (ƒ - g)(-1), you first calculate ƒ(-1) and g(-1) using their respective formulas, then subtract the results. This process is crucial for determining the value of the combined function at a given input.