Chapter 1
Linear Equations and Graphing
Course: Gre
Subject: Gre Quantitative Reasoning
Chapter: Quadratic Equations And Polynomials
Introduction: Combining Functions
Just as numbers can be added, subtracted, multiplied, and divided, functions can be combined through operations. These operations create new functions that can be evaluated, analyzed, and used in applications.
This lesson explores how to perform operations with functions and how to determine the domain of the resulting functions.
Function Operations
Given two functions f(x) and g(x), several operations can be performed:
| Operation | Notation | Result | | Addition | (f + g)(x) | f(x) + g(x) | | Subtraction | (f - g)(x) | f(x) - g(x) | | Multiplication | (f × g)(x) | f(x) × g(x) | | Division | (f / g)(x) | f(x) / g(x) | | Composition | (f ∘ g)(x) | f(g(x)) |
Example 1: Function Composition from a Graph