3.8 Inverse Functions

Mr. Wilhelm taught us about inverse functions ever so perfectly, but the wheel has chosen me to sum it up.

Two function, f and g, are inverses of each other if and only if
                               

One-to-One
A function is one-to-one if it passes the horizontal line test (every horizontal line intersects the graph in at most one point) and if

 -----> 

3a+2=3b+2

3a=3b

a=b

A function that is increasing throughout its domain is one-to-one.

A function that is decreasing throughout its domain is one-to-one.

Finding

1) Verify that f is a one-to-one function

2) Solve the equation y=f(x) for x in terms of y, obtaining an equation of the form                     

x=(y)

3) Verify that:

 for every x in the domain of f

 for every x in the domain of 

There are many examples in the book if you need them.

Remember, always keep the Wilhelm philosophy in mind, "Learn and the grades will follow," and "Eleni is always right."

HAPPY BIRTHDAY THAD!

Joseph "The Preston" Nagridge