Chapter 1
Linear Equations and Graphing
Course: Gre
Subject: Gre Quantitative Reasoning
Chapter: Quadratic Equations And Polynomials
Introduction: The Opposite of a Function
If addition and subtraction are opposites, and multiplication and division are opposites, then functions have opposites too. An inverse function does exactly the opposite of the original function: it undoes what the original function did.
If a function takes an input, adds 3, and divides by 4, its inverse would multiply by 4 and subtract 3.
What Is an Inverse Function?
The inverse of a function f(x)is denoted f-1(x). Important: f-1(x)is not the same as 1f(x). The -1is not an exponent; it indicates the inverse function.
Key Property
For inverse functions:
f-1(f(x))=xand f(f-1(x))=x
When a function and its inverse are composed, they "undo" each other, returning the original input.
How to Find the Inverse of a Function
Method 1: Using Inverse Operations
List the steps the original function performs. Then, working backward from the last step to the first, list the inverse of each step.