Inverses and How to Find Them

2.9: Inverses & How to Find Them (Equation)By: Hans Seebaluck

Basics!One-to-One: A function with domain A is called one-to-one if no 2 elements of A have the same image (y-value).How do you know if a function is One-to-One?A function is One-to-One if it passes the HORIZONTAL LINE TEST.

Examples: Passing :)

These two pass because the horizontal line only crosses the function once!

Examples: Failing :(

These two fail because the horizontal line crosses the function at 2 or more different points!

How to find the inverse of a function:

Step 1: Flip roles of "x" and "y"Ex: y=2x+1---> x=2y+1

Step 2: Solve for "y"x=2y+1 ---> x-1=2y ---> (x-1)/2=yStep 3: y=(x-1)/2 is the inverse of the original equation

-1

Original: f(x)

Inverse: f (x)

Another Example